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Q.

If a represents the number of permutations of (x + 2) things taken together, b represents the number of permutations of 11 things taken together out of x things, and c represents the number of permutations of (x – 11) things taken together so that a = 182bc, then x =

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a

15

b

12

c

10

d

18

answer is B.

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Detailed Solution

a=x+2Px+2,b=xP11,C=x−11Px−11⇒ a=(x+2)!,b=x!(x−11)!,c=(x−11)!Now, a = 182 bc⇒(x+2)!=182x!(x−11)!(x−11)!⇒(x+2)(x+1)x!=182x!⇒(x+2)(x+1)=182=14×13⇒x+1=13∴x=12

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