Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ Question 9: In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student? Solution 9: There are 9 courses available out of which, 2 specific courses are compulsory for every student. Therefore, every student has to choose 3 courses out of the remaining 7 courses. This can be chosen in 7 C 3 ways. Thus, required number of ways of choosing the programme 7! 765 4! 3!4! 3 21 4! 7 C3 35 . Miscellaneous Exercise Question 1: How many words, with or without meaning , each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Solution 1: In the word DAUGHTER, there are 3 vowels namely, A, U, and E and 5 consonants, namely, D, G, H, T, and R. Number of ways of selecting 2 vowels of 3 vowels 3 C 2 3 Number of ways of selecting 3 consonants out of 5 consonants 5 C 3 10 310 30 Therefore, number of combinations of 2 vowels and 3 consonants Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways. Hence, required number of different words . 35! 3600 Question 2: How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together? Solution 2: In the word EQUATION, there are 5 vowels, namely, A, E, I, O and U and 3 consonants, namely Q, T and N. Since all the vowels and consonants have to occur together, both (AEIOU) and (QTN) can be Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ assumed as single objects. Then, the permutations of these 2 objects taken all at a time are counted. This number would be 2 P2 2! Corresponding to each of these permutations, there are 5! Permutations of the five vowels taken all at a time and 3! Permutations of the 3 consonants taken all at a time. Hence, by multiplication principle, required number of words . 2! 5! 3! 1440 Question 3: A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) Atleast 3 girls? (iii) atmost 3 girls? Solution 3: (i) A committee of 7 has to be formed from 9 boys and 4 girls. Since exactly 3 girls are to be there in every committee, each committee must consist of 7 3 4 boys only. Thus, in this case, required number of ways 98 7 65! 4 43 25! 4 9 4! 9! C3 C4 3!1! 4!5! 504 (ii) Since at least 3 girls are to be there in every committee, the committee can consist of (a) 3 girls and 4 boys or (b) 4 girls and 3 boys 3 girls and 4 boys can be selected in 4 girls and 3 boys can be selected in C C 4 9 3 4 C C 4 9 4 3 Therefore, in this case, required number of ways ways. ways. C C C C 4 9 4 9 3 4 4 3 504 84 588 (iii) Since atmost 3 girls are to be there in every committee, the committee can consist of (a) 3 girls and 4 boys (b) 2 girls and 5 boys (c) 1 girl and 6 boys (d) No girl and 7 boys 3 girls and 4 boys can be selected in 4 C 9 C ways. 3 4 2 girls and 5 boys can be selected in 4 C 9 C ways. 1 girl and 6 boys can be selected in C 2 5 C 4 9 1 6 ways. No girl and 7 boys can be selected in 4 C 9 C ways. 0 7 Therefore, in this case, required number of ways Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

- Page 1 and 2:
Class XI Chapter 1 - Sets Maths ___

- Page 3 and 4:
Class XI Chapter 1 - Sets Maths ___

- Page 5 and 6:
Class XI Chapter 1 - Sets Maths ___

- Page 7 and 8:
Class XI Chapter 1 - Sets Maths ___

- Page 9 and 10:
Class XI Chapter 1 - Sets Maths ___

- Page 11 and 12:
Class XI Chapter 1 - Sets Maths ___

- Page 13 and 14:
Class XI Chapter 1 - Sets Maths ___

- Page 15 and 16:
Class XI Chapter 1 - Sets Maths ___

- Page 17 and 18:
Class XI Chapter 1 - Sets Maths ___

- Page 19 and 20:
Class XI Chapter 1 - Sets Maths ___

- Page 21 and 22:
Class XI Chapter 1 - Sets Maths ___

- Page 23 and 24:
Class XI Chapter 1 - Sets Maths ___

- Page 25 and 26:
Class XI Chapter 1 - Sets Maths ___

- Page 27 and 28:
Class XI Chapter 1 - Sets Maths ___

- Page 29 and 30:
Class XI Chapter 1 - Sets Maths ___

- Page 31 and 32:
Class XI Chapter 1 - Sets Maths ___

- Page 33 and 34:
Class XI Chapter 1 - Sets Maths ___

- Page 35 and 36:
Class XI Chapter 1 - Sets Maths ___

- Page 37 and 38:
Class XI Chapter 1 - Sets Maths ___

- Page 39 and 40:
Class XI Chapter 1 - Sets Maths ___

- Page 41 and 42:
Class XI Chapter 1 - Sets Maths ___

- Page 43 and 44:
Class XI Chapter 2 - Relations and

- Page 45 and 46:
Class XI Chapter 2 - Relations and

- Page 47 and 48:
Class XI Chapter 2 - Relations and

- Page 49 and 50:
Class XI Chapter 2 - Relations and

- Page 51 and 52:
Class XI Chapter 2 - Relations and

- Page 53 and 54:
Class XI Chapter 2 - Relations and

- Page 55 and 56:
Class XI Chapter 2 - Relations and

- Page 57 and 58:
Class XI Chapter 2 - Relations and

- Page 59 and 60:
Class XI Chapter 2 - Relations and

- Page 61 and 62:
Class XI Chapter 3 - Trigonometric

- Page 63 and 64:
Class XI Chapter 3 - Trigonometric

- Page 65 and 66:
Class XI Chapter 3 - Trigonometric

- Page 67 and 68:
Class XI Chapter 3 - Trigonometric

- Page 69 and 70:
Class XI Chapter 3 - Trigonometric

- Page 71 and 72:
Class XI Chapter 3 - Trigonometric

- Page 73 and 74:
Class XI Chapter 3 - Trigonometric

- Page 75 and 76:
Class XI Chapter 3 - Trigonometric

- Page 77 and 78:
Class XI Chapter 3 - Trigonometric

- Page 79 and 80:
Class XI Chapter 3 - Trigonometric

- Page 81 and 82:
Class XI Chapter 3 - Trigonometric

- Page 83 and 84:
Class XI Chapter 3 - Trigonometric

- Page 85 and 86:
Class XI Chapter 3 - Trigonometric

- Page 87 and 88:
Class XI Chapter 3 - Trigonometric

- Page 89 and 90:
Class XI Chapter 3 - Trigonometric

- Page 91 and 92:
Class XI Chapter 3 - Trigonometric

- Page 93 and 94:
Class XI Chapter 3 - Trigonometric

- Page 95 and 96:
Class XI Chapter 3 - Trigonometric

- Page 97 and 98:
Class XI Chapter 3 - Trigonometric

- Page 99 and 100:
Class XI Chapter 4 - Principle of M

- Page 101 and 102:
Class XI Chapter 4 - Principle of M

- Page 103 and 104:
Class XI Chapter 4 - Principle of M

- Page 105 and 106:
Class XI Chapter 4 - Principle of M

- Page 107 and 108:
Class XI Chapter 4 - Principle of M

- Page 109 and 110:
Class XI Chapter 4 - Principle of M

- Page 111 and 112:
Class XI Chapter 4 - Principle of M

- Page 113 and 114:
Class XI Chapter 4 - Principle of M

- Page 115 and 116:
Class XI Chapter 4 - Principle of M

- Page 117 and 118:
Class XI Chapter 4 - Principle of M

- Page 119 and 120:
Class XI Chapter 4 - Principle of M

- Page 121 and 122:
Class XI Chapter 4 - Principle of M

- Page 123 and 124:
Class XI Chapter 4 - Principle of M

- Page 125 and 126:
Class XI Chapter 5 - Complex Number

- Page 127 and 128:
Class XI Chapter 5 - Complex Number

- Page 129 and 130:
Class XI Chapter 5 - Complex Number

- Page 131 and 132:
Class XI Chapter 5 - Complex Number

- Page 133 and 134:
Class XI Chapter 5 - Complex Number

- Page 135 and 136:
Class XI Chapter 5 - Complex Number

- Page 137 and 138:
Class XI Chapter 5 - Complex Number

- Page 139 and 140:
Class XI Chapter 5 - Complex Number

- Page 141 and 142:
Class XI Chapter 5 - Complex Number

- Page 143 and 144:
Class XI Chapter 5 - Complex Number

- Page 145 and 146:
Class XI Chapter 5 - Complex Number

- Page 147 and 148:
Class XI Chapter 5 - Complex Number

- Page 149 and 150:
Class XI Chapter 5 - Complex Number

- Page 151 and 152:
Class XI Chapter 5 - Complex Number

- Page 153 and 154:
Class XI Chapter 5 - Complex Number

- Page 155 and 156:
Class XI Chapter 6 - Linear Inequal

- Page 157 and 158:
Class XI Chapter 6 - Linear Inequal

- Page 159 and 160:
Class XI Chapter 6 - Linear Inequal

- Page 161 and 162: Class XI Chapter 6 - Linear Inequal
- Page 163 and 164: Class XI Chapter 6 - Linear Inequal
- Page 165 and 166: Class XI Chapter 6 - Linear Inequal
- Page 167 and 168: Class XI Chapter 6 - Linear Inequal
- Page 169 and 170: Class XI Chapter 6 - Linear Inequal
- Page 171 and 172: Class XI Chapter 6 - Linear Inequal
- Page 173 and 174: Class XI Chapter 6 - Linear Inequal
- Page 175 and 176: Class XI Chapter 6 - Linear Inequal
- Page 177 and 178: Class XI Chapter 6 - Linear Inequal
- Page 179 and 180: Class XI Chapter 6 - Linear Inequal
- Page 181 and 182: Class XI Chapter 6 - Linear Inequal
- Page 183 and 184: Class XI Chapter 6 - Linear Inequal
- Page 185 and 186: Class XI Chapter 6 - Linear Inequal
- Page 187 and 188: Class XI Chapter 6 - Linear Inequal
- Page 189 and 190: Class XI Chapter 6 - Linear Inequal
- Page 191 and 192: Class XI Chapter 6 - Linear Inequal
- Page 193 and 194: Class XI Chapter 6 - Linear Inequal
- Page 195 and 196: Class XI Chapter 6 - Linear Inequal
- Page 197 and 198: Class XI Chapter 7 - Permutation an
- Page 199 and 200: Class XI Chapter 7 - Permutation an
- Page 201 and 202: Class XI Chapter 7 - Permutation an
- Page 203 and 204: Class XI Chapter 7 - Permutation an
- Page 205 and 206: Class XI Chapter 7 - Permutation an
- Page 207 and 208: Class XI Chapter 7 - Permutation an
- Page 209 and 210: Class XI Chapter 7 - Permutation an
- Page 211: Class XI Chapter 7 - Permutation an
- Page 215 and 216: Class XI Chapter 7 - Permutation an
- Page 217 and 218: Class XI Chapter 7 - Permutation an
- Page 219 and 220: Class XI Chapter 8 - Binomial Theor
- Page 221 and 222: Class XI Chapter 8 - Binomial Theor
- Page 223 and 224: Class XI Chapter 8 - Binomial Theor
- Page 225 and 226: Class XI Chapter 8 - Binomial Theor
- Page 227 and 228: Class XI Chapter 8 - Binomial Theor
- Page 229 and 230: Class XI Chapter 8 - Binomial Theor
- Page 231 and 232: Class XI Chapter 8 - Binomial Theor
- Page 233 and 234: Class XI Chapter 8 - Binomial Theor
- Page 235 and 236: Class XI Chapter 8 - Binomial Theor
- Page 237 and 238: Class XI Chapter 8 - Binomial Theor
- Page 239 and 240: Class XI Chapter 8 - Binomial Theor
- Page 241 and 242: Class XI Chapter 9 - Sequences and
- Page 243 and 244: Class XI Chapter 9 - Sequences and
- Page 245 and 246: Class XI Chapter 9 - Sequences and
- Page 247 and 248: Class XI Chapter 9 - Sequences and
- Page 249 and 250: Class XI Chapter 9 - Sequences and
- Page 251 and 252: Class XI Chapter 9 - Sequences and
- Page 253 and 254: Class XI Chapter 9 - Sequences and
- Page 255 and 256: Class XI Chapter 9 - Sequences and
- Page 257 and 258: Class XI Chapter 9 - Sequences and
- Page 259 and 260: Class XI Chapter 9 - Sequences and
- Page 261 and 262: Class XI Chapter 9 - Sequences and
- Page 263 and 264:
Class XI Chapter 9 - Sequences and

- Page 265 and 266:
Class XI Chapter 9 - Sequences and

- Page 267 and 268:
Class XI Chapter 9 - Sequences and

- Page 269 and 270:
Class XI Chapter 9 - Sequences and

- Page 271 and 272:
Class XI Chapter 9 - Sequences and

- Page 273 and 274:
Class XI Chapter 9 - Sequences and

- Page 275 and 276:
Class XI Chapter 9 - Sequences and

- Page 277 and 278:
Class XI Chapter 9 - Sequences and

- Page 279 and 280:
Class XI Chapter 9 - Sequences and

- Page 281 and 282:
Class XI Chapter 9 - Sequences and

- Page 283 and 284:
Class XI Chapter 9 - Sequences and

- Page 285 and 286:
Class XI Chapter 9 - Sequences and

- Page 287 and 288:
Class XI Chapter 9 - Sequences and

- Page 289 and 290:
Class XI Chapter 9 - Sequences and

- Page 291 and 292:
Class XI Chapter 9 - Sequences and

- Page 293 and 294:
Class XI Chapter 9 - Sequences and

- Page 295 and 296:
Class XI Chapter 9 - Sequences and

- Page 297 and 298:
Class XI Chapter 9 - Sequences and

- Page 299 and 300:
Class XI Chapter 9 - Sequences and

- Page 301 and 302:
Class XI Chapter 9 - Sequences and

- Page 303 and 304:
Class XI Chapter 9 - Sequences and

- Page 305 and 306:
Class XI Chapter 9 - Sequences and

- Page 307 and 308:
Class XI Chapter 9 - Sequences and

- Page 309 and 310:
Class XI Chapter 9 - Sequences and

- Page 311 and 312:
Class XI Chapter 9 - Sequences and

- Page 313 and 314:
Class XI Chapter 10 - Straight Line

- Page 315 and 316:
Class XI Chapter 10 - Straight Line

- Page 317 and 318:
Class XI Chapter 10 - Straight Line

- Page 319 and 320:
Class XI Chapter 10 - Straight Line

- Page 321 and 322:
Class XI Chapter 10 - Straight Line

- Page 323 and 324:
Class XI Chapter 10 - Straight Line

- Page 325 and 326:
Class XI Chapter 10 - Straight Line

- Page 327 and 328:
Class XI Chapter 10 - Straight Line

- Page 329 and 330:
Class XI Chapter 10 - Straight Line

- Page 331 and 332:
Class XI Chapter 10 - Straight Line

- Page 333 and 334:
Class XI Chapter 10 - Straight Line

- Page 335 and 336:
Class XI Chapter 10 - Straight Line

- Page 337 and 338:
Class XI Chapter 10 - Straight Line

- Page 339 and 340:
Class XI Chapter 10 - Straight Line

- Page 341 and 342:
Class XI Chapter 10 - Straight Line

- Page 343 and 344:
Class XI Chapter 10 - Straight Line

- Page 345 and 346:
Class XI Chapter 10 - Straight Line

- Page 347 and 348:
Class XI Chapter 10 - Straight Line

- Page 349 and 350:
Class XI Chapter 10 - Straight Line

- Page 351 and 352:
Class XI Chapter 10 - Straight Line

- Page 353 and 354:
Class XI Chapter 10 - Straight Line

- Page 355 and 356:
Class XI Chapter 10 - Straight Line

- Page 357 and 358:
Class XI Chapter 10 - Straight Line

- Page 359 and 360:
Class XI Chapter 10 - Straight Line

- Page 361 and 362:
Class XI Chapter 10 - Straight Line

- Page 363 and 364:
Class XI Chapter 10 - Straight Line

- Page 365 and 366:
Class XI Chapter 10 - Straight Line

- Page 367 and 368:
Class XI Chapter 10 - Straight Line

- Page 369 and 370:
Class XI Chapter 10 - Straight Line

- Page 371 and 372:
Class XI Chapter 10 - Straight Line

- Page 373 and 374:
Class XI Chapter 11 - Conic Section

- Page 375 and 376:
Class XI Chapter 11 - Conic Section

- Page 377 and 378:
Class XI Chapter 11 - Conic Section

- Page 379 and 380:
Class XI Chapter 11 - Conic Section

- Page 381 and 382:
Class XI Chapter 11 - Conic Section

- Page 383 and 384:
Class XI Chapter 11 - Conic Section

- Page 385 and 386:
Class XI Chapter 11 - Conic Section

- Page 387 and 388:
Class XI Chapter 11 - Conic Section

- Page 389 and 390:
Class XI Chapter 11 - Conic Section

- Page 391 and 392:
Class XI Chapter 11 - Conic Section

- Page 393 and 394:
Class XI Chapter 11 - Conic Section

- Page 395 and 396:
Class XI Chapter 11 - Conic Section

- Page 397 and 398:
Class XI Chapter 11 - Conic Section

- Page 399 and 400:
Class XI Chapter 11 - Conic Section

- Page 401 and 402:
Class XI Chapter 11 - Conic Section

- Page 403 and 404:
Class XI Chapter 11 - Conic Section

- Page 405 and 406:
Class XI Chapter 11 - Conic Section

- Page 407 and 408:
Class XI Chapter 11 - Conic Section

- Page 409 and 410:
Class XI Chapter 11 - Conic Section

- Page 411 and 412:
Class XI Chapter 11 - Conic Section

- Page 413 and 414:
Class XI Chapter 11 - Conic Section

- Page 415 and 416:
Class XI Chapter 11 - Conic Section

- Page 417 and 418:
Class XI Chapter 12 - Introduction

- Page 419 and 420:
Class XI Chapter 12 - Introduction

- Page 421 and 422:
Class XI Chapter 12 - Introduction

- Page 423 and 424:
Class XI Chapter 12 - Introduction

- Page 425 and 426:
Class XI Chapter 12 - Introduction

- Page 427 and 428:
Class XI Chapter 12 - Introduction

- Page 429 and 430:
Class XI Chapter 12 - Introduction

- Page 431 and 432:
Class XI Chapter 13 - Limits and De

- Page 433 and 434:
Class XI Chapter 13 - Limits and De

- Page 435 and 436:
Class XI Chapter 13 - Limits and De

- Page 437 and 438:
Class XI Chapter 13 - Limits and De

- Page 439 and 440:
Class XI Chapter 13 - Limits and De

- Page 441 and 442:
Class XI Chapter 13 - Limits and De

- Page 443 and 444:
Class XI Chapter 13 - Limits and De

- Page 445 and 446:
Class XI Chapter 13 - Limits and De

- Page 447 and 448:
Class XI Chapter 13 - Limits and De

- Page 449 and 450:
Class XI Chapter 13 - Limits and De

- Page 451 and 452:
Class XI Chapter 13 - Limits and De

- Page 453 and 454:
Class XI Chapter 13 - Limits and De

- Page 455 and 456:
Class XI Chapter 13 - Limits and De

- Page 457 and 458:
Class XI Chapter 13 - Limits and De

- Page 459 and 460:
Class XI Chapter 13 - Limits and De

- Page 461 and 462:
Class XI Chapter 13 - Limits and De

- Page 463 and 464:
Class XI Chapter 13 - Limits and De

- Page 465 and 466:
Class XI Chapter 13 - Limits and De

- Page 467 and 468:
Class XI Chapter 13 - Limits and De

- Page 469 and 470:
Class XI Chapter 13 - Limits and De

- Page 471 and 472:
Class XI Chapter 13 - Limits and De

- Page 473 and 474:
Class XI Chapter 13 - Limits and De

- Page 475 and 476:
Class XI Chapter 13 - Limits and De

- Page 477 and 478:
Class XI Chapter 13 - Limits and De

- Page 479 and 480:
Class XI Chapter 13 - Limits and De

- Page 481 and 482:
Class XI Chapter 13 - Limits and De

- Page 483 and 484:
Class XI Chapter 13 - Limits and De

- Page 485 and 486:
Class XI Chapter 13 - Limits and De

- Page 487 and 488:
Class XI Chapter 13 - Limits and De

- Page 489 and 490:
Class XI Chapter 13 - Limits and De

- Page 491 and 492:
Class XI Chapter 14 - Mathematical

- Page 493 and 494:
Class XI Chapter 14 - Mathematical

- Page 495 and 496:
Class XI Chapter 14 - Mathematical

- Page 497 and 498:
Class XI Chapter 14 - Mathematical

- Page 499 and 500:
Class XI Chapter 14 - Mathematical

- Page 501 and 502:
Class XI Chapter 14 - Mathematical

- Page 503 and 504:
Class XI Chapter 14 - Mathematical

- Page 505 and 506:
Class XI Chapter 14 - Mathematical

- Page 507 and 508:
Class XI Chapter 15 - Statistics Ma

- Page 509 and 510:
Class XI Chapter 15 - Statistics Ma

- Page 511 and 512:
Class XI Chapter 15 - Statistics Ma

- Page 513 and 514:
Class XI Chapter 15 - Statistics Ma

- Page 515 and 516:
Class XI Chapter 15 - Statistics Ma

- Page 517 and 518:
Class XI Chapter 15 - Statistics Ma

- Page 519 and 520:
Class XI Chapter 15 - Statistics Ma

- Page 521 and 522:
Class XI Chapter 15 - Statistics Ma

- Page 523 and 524:
Class XI Chapter 15 - Statistics Ma

- Page 525 and 526:
Class XI Chapter 15 - Statistics Ma

- Page 527 and 528:
Class XI Chapter 15 - Statistics Ma

- Page 529 and 530:
Class XI Chapter 15 - Statistics Ma

- Page 531 and 532:
Class XI Chapter 15 - Statistics Ma

- Page 533 and 534:
Class XI Chapter 15 - Statistics Ma

- Page 535:
Class XI Chapter 15 - Statistics Ma

Loading...

Thank you, for helping us keep this platform clean.

The editors will have a look at it as soon as possible.

Loading...

Loading...

Are you sure you want to delete your template?

**Magazine:** CLASS_11_MATHS_SOLUTIONS_NCERT

Start using Yumpu now!