Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ C C C C C C C C 4 9 4 9 4 9 4 9 3 4 2 5 1 6 0 7 4! 9! 4! 9! 4! 9! 4! 9! 3!1! 4!5! 2!2! 5!4! 1!3! 6!3! 0!4! 7!2! 504 756 336 36 1632 Question 4: If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in list before the first word starting with E? Solution 4: In the given word EXAMINATION, there are **11** letters out of which, A, I and N appear 2 times and all the other letters appear only once. The words that will be listed before the words starting with E in a dictionary will be the words that start with A only. Therefore, to get the number of words starting with A, the letter A is fixed at the extreme left position, and then the remaining 10 letters taken all at a time are rearranged. Since there are 2 Is and 2 Ns in the remaining 10 letters, Number of words starting with 10! A 907200 2!2! Thus, the required numbers of words is 907200. Question 5: How many 6-digit numbers can be formed from the digits, 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated? Solution 5: A number is divisible by 10 if its units digits is 0. Therefore, 0 is fixed at the units place. Therefore, there will be as many ways as there are ways of filling 5 vacant places in succession by the remaining 5 digits (i.e., 1, 3, 5, 7 and 9). The 5 vacant places can be filled in 5! Ways. Hence, required number of 6-digit numbers 5! 120 0 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 ______________________________________________________________________________ Question 6: The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet? Solution 6: 2 different vowels and 2 different consonants are to be selected from the English alphabet. Since there are 5 vowels in the English alphabet, number of ways of selecting 2 different vowels from the alphabet 5! 2!3! 5 C2 10 Since there are 21 consonants in the English alphabet, number of ways of selecting 2 different consonants from the alphabet 21! 2!19! 21 C2 210 Therefore, number of combinations of 2 different vowels and 2 different consonants 10 210 2100 Each of these 2100 combinations has 4 letters, which can be arranged among themselves in 4! ways. Therefore, required number of words 2100 4! 50400 . Question 7: In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions? Solution 7: It is given that the question paper consists of 12 questions divided into two parts – Part I and Part II, containing 5 and 7 questions, respectively. A student has to attempt 8 questions, selecting at least 3 from each part. This can be done as follows. (a) 3 questions from part I and 5 questions from part II (b) 4 questions from part I and 4 questions from part II (c) 5 questions from part I and 3 questions from part II 3 questions from part I and 5 questions from part II can be selected in C C 5 7 3 5 ways. 4 questions from part I and 4 questions from part II can be selected in 5 C 7 C ways. 4 4 5 questions from part I and 3 questions from part II can be selected in 5 C 7 5 C3 ways. Thus, required number of ways of selecting questions C C C C C C 5 7 5 7 5 7 3 5 4 4 5 3 5! 7! 5! 7! 5! 7! 2!3! 2!5! 4!1! 4!3! 5!0! 3!4! 210 175 35 420 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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