If 'a' denotes the number of permutations of (x+2) things taken all at a time, 'b' the number of permutations - Maths - Permutations and Combinations

Question

If 'a' denotes the number of permutations of (x+2) things taken
all at a time, 'b' the number of permutations of 'x' things taken
11 at a time and 'c' the number of permutaions of (X-11) things
taken all at a time such that a=182bc, find the value of x??

Prasanta · Accepted Answer

It is given that,

a=Px+2x+2=x+2!

b=P11x=x!x-11!

c=Px-11x-11=x-11!

Also, a=182bc

⇒x+2!=182 x!x-11! x-11!⇒x+2x+1=182

⇒x2+3x-180=0⇒x-12x+15=0⇒x=12, or, x=-15

If 'a' denotes the number of permutations of (x+2) things taken all at a time, 'b' the number of permutations of 'x' things taken 11 at a time and 'c' the number of permutaions of (X-11) things taken all at a time such that a=182bc, find the value of x??