Question

Value of r when ${}^{10}{P}_r=720$ is :

• A. 3
• B. 7
• C. 5
• D. None of these

Answer 1

Answer: (A)

3

$10P_r=720$

$\Rightarrow \frac{10!}{(10-r)!}=720$ $[\because \frac{n!}{(n-n)!}]$

$\Rightarrow (10-r)!=\frac{10!}{720}$

$\Rightarrow (10-r)!=\frac{3628800}{720}$

$\Rightarrow (10-r)!=5040$

$\Rightarrow (10-r)\times (9-r)\times (8-r)\times .....\times 1=7\times 6\times 5\times 4\times 3\times 2\times 1$

$\Rightarrow 10-r=7$

$\Rightarrow r=10-7=3$

or

$\Rightarrow 9-r=6$

$\Rightarrow r=9-6=3$

Hence $r=3$