Question

If ${}^{10}{P}_r$ = 5040, then the value of r is

• A. 2
• B. 3
• C. 4
• D. none of these

Answer 1

The correct option is C 4

Given $10P_r=5040$

$\frac{10!}{(10-r)!}=5040$ [$10P_r=\frac{10!}{(10-r)!}$ from ${}^n{P}_r=\frac{n!}{(n-r)!}$]

$=(10-r)!=\frac{10!}{5040}$

$=\frac{10\times 9\times 8\times 7\times 6!}{7\times 720}$ $[6!=720]$

$=\frac{10\times 9\times 8\times 7\times 720}{7\times 720}$

$=720$

$(10-r)!=6!$

$10-r=6$

$r=10-6$

$r=4$.