If C r + 1 n + 1 : C r n : C r - 1 n - 1 = 11 : 6 : 3 , then find the values of n and r .

Given C r + 1 n + 1 : C r n : C r - 1 n - 1 = 11 : 6 : 3 Firstly take, C r + 1 n + 1 : C r n = 11 6 ⇒ n + 1 ! r + 1 ! n - r ! × r ! n - r ! n ! = 11 6 ⇒ n + 1 r + 1 = 11 6 ⇒ 6 n + 6 = 11 r + 11 ⇒ 6 n - 11 r = 5 . . . . . . . . i And now take, C r n : C r - 1 n - 1 = 6 : 3 ⇒ n ! r ! n - r ! × r - 1 ! n - r ! n - 1 ! = 2 ⇒ n = 2 r . . . . . . . . i i Put value of n from i in i i ⇒ 6 2 r - 11 r = 5 ⇒ r = 5 , n = 10

If P 2 m + n = 90 and P 2 m - n = 30 , then find m , n .

Given P 2 m + n = 90 ⇒ m + n ! m + n - 2 ! = 90 ⇒ m + n m + n - 1 = 90 Let m + n = p ⇒ p × p - 1 = 90 ⇒ p = 10 Also P 2 m - n = 30 ⇒ m - n ! m - n - 2 ! = 30 ⇒ m - n m - n - 1 = 30 Let m - n = q ⇒ q × q - 1 = 30 ⇒ q = 6 So, m + n = 10 , m - n = 6 ⇒ 2 m = 16 ⇒ m = 8 , n = 2 Therefore m , n = 8 , 2

If C 8 n + 2 : P 4 n - 2 = 57 : 16 , prove that n = 19 .

Given C 8 n + 2 : P 4 n - 2 = 57 : 16 ⇒ n + 2 ! 8 ! n - 6 ! × n - 6 ! n - 2 ! = 57 16 ⇒ n + 2 n + 1 n n - 1 8 ! = 57 16 ⇒ n + 2 n + 1 n n - 1 = 143640 ⇒ n + 2 n + 1 n n - 1 = 21 × 20 × 19 × 18 So by this we can conclude that n = 19

E M B I B E

Gamma Question Bank for Engineering Mathematics>Class XI>Chapter 7 - Permutations and Combinations>Assignment

Embibe Experts Solutions for Exercise 6: Assignment

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Exercise 6: Assignment

Attempt the free practice questions from Exercise 6: Assignment with hints and solutions to strengthen your understanding. Gamma Question Bank for Engineering Mathematics solutions are prepared by Experienced Embibe Experts.