Question

If ${}^{12}{P}_r=1320$, then r is equal to

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is C 3

Given:- ${}^{12}{P}_r=1320$

To find:- $r=?$

As we know that,

${}^n{P}_r=\frac{n!}{(n-r)!}$

Therefore,

${}^{12}{P}_r=1320$

$\frac{12!}{(12-r)!}=1320$

$\Rightarrow (12-r)!=\frac{12\times 11\times 10\times 9!}{12\times 11\times 10}(\because 1320=12\times 11\times 10)$

$\Rightarrow (12-r)!=9!$

$\Rightarrow 12-r=9$

$\Rightarrow r=12-9=3$

Hence the value of $r$ is $3$

Hence the correct answer is $\left(C\right)3$.