Question

If ${}^n{P}_r=$ $30240$ and ${}^n{C}_r=$ $252$, then the ordered pair $(n,r)$ $=$

• A. $(12,6)$
• B. $(10,5)$
• C. $(9,4)$
• D. $(16,7)$

Answer 1

Answer: (B)

$(10,5)$

Given, ${}^n{P}_r=30240$ and ${}^n{C}_r=252$

We know, $\frac{{}^n{P}_r}{{}^n{C}_r}=r!=\frac{30240}{252}=120=5!$

$\Rightarrow r=5$
$\Rightarrow (n,r)=(10,5)$