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If a denotes the number of permutations ...

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 permutations of (x-11) things taken all at a time such that a=182 bc, the value of x is

A

15

B

12

C

10

D

18

Text Solution

Verified by Experts

The correct Answer is:
B
`because a=182bc`
`implies(x+2)!=182xx.^(x)P_(11)xx(x-11)!`
`implies(x+2)!=182xx x!`
`implies(x+2)(x+1)=14xx13` ,brgt `impliesx+1=13`
`thereforex=12`
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