Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ Question 7: Find r if (i) 5 6 Pr 2 P r 1 Solution 7: (i) 5 6 Pr 2 P r 1 (ii) 5! 6! 2 5 ! 6 1 ! r r 5! 26! 5 ! 7 ! r r 5 6 Pr Pr 1 5! 65! 5 ! 7 6 5 ! r r r r 1 26 7r6r 7 r 6 r 12 2 42 6r 7r r 12 2 r r 13 30 0 2 r r r 3 10 30 0 r r 3 10 r 3 0 r r 3 10 0 r r 3 0 or 10 0 r 3 or r 10 It is known that, 0 r 5 r (ii) 3 5 6 P r Pr 1 n P 5! 6! 5 r ! 6 r1 ! 5! 65! 5 ! 7 ! r r r n! n r ! 5! 6 5 ! 7 6 5 ! r r r r , where 0 r n 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 ______________________________________________________________________________ 1 6 7r6r r r 7 6 6 2 42 7r 6r r 6 0 2 r r 13 36 0 2 r r r 4 9 36 0 r r r 4 9 4 0 r r 4 9 0 r r 4 0 or 9 0 r 4 or r 9 It is known that, 0 r 5 Hence, r 4 r 9 n P r n! n r ! , where 0 r n Question 8: How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once? Solution 8: There are 8 different letters in the word EQUATION. Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once, is the number of permutations of 8 different objects taken 8 at a time, which is 8 P8 8! . Thus, required number of words that can be formed 8! 40320 Question 9: How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel? Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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