Question

If p denotes the number of permutations of n + 2 things taken all at a time, q the number of permutations of n things taken 11 at a time and r the number of permutations of n – 11 things taken all at a time such that p = 182 qr, then the value of n is
A) 15
B) 12
C) 10
D) 18

Answer 1

Answer:

Step-by-step explanation:

Let p denote the no. of permutations of (n+2) things taken all at a time

Therefore,p = n+2Pn+2 = (n+2)!                    

Let q denote the no. of permutations of n things taken 11 at a time

Therefore, q = nP11 = n!/(n-11)!

Let r denote the no. of permutations of (n-11) things taken all at a time

Hence, r = n-11Pn-11 = (n - 11)!

And P=182qr

Substituting for the value of p,q, and r to obtain;

(n+2)! = 182* n!/(n-11)!  * (n- 11)!

(n+2)*(n+1)*n! = 182*n!

(n+2)*(n+1) = 182

n^2 + 3n + 2 = 182

n^2 + 3n + 2 - 182 = 0

n^2 + 3n - 180 = 0

(n-12)*(n+15) = 0

Therefore, n = 12, -15

The value of n is 12

(B) 12

Answer 2

Answer:

I hope this is the correct answer ☺️