Question

'p' denotes the number of permutation of x+3 things taken all at a time 'q' denotes the number of permutation of x+1 things taken 11 at atime and 'r' denotes the number of permutation of x-10 things all at a time and that p=182qr find x?​

Answer 1

Step-by-step explanation:

Given that p denotes the number of permutations of (x+3) things all at a time.

⇒p=

x+3

P

x+3

=(x+3)!

q denotes the number of permutations of (x+1) things taken 11 at a time.

⇒q=

x+1

P

11

=

((x+1)−11)!

(x+1)!

r denotes the number of permutations of (x−10) things taken 11 at a time.

⇒r=

x−10

P

x−10

=(x−10)!

Given that,

p=182qr

Put the values of p, q and r, we get,

(x+3)!=182×

(x−10)!

(x+1)!

×(x−10)!

⇒(x+3)!=182×(x+1)!

(x+3)(x+2)(x+1)!=182×(x+1)!

(x+3)(x+2)=182

x

2

+5x+6=182

x

2

+5x−176=0

(x−11)(x+16)=0

x=11,−16

Values of x =11,−16