Question

If ${}^{10}{p}_{r+1}:{}^{11}{p}_r=30:11$, find the value of $r$

Answer 1

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

$\frac{\frac{10!}{(9-r)!}}{\frac{11!}{(11-r)!}}=\frac{30}{11}$

On solving this we get $r=16,5$

But $r=16$not possible so $r=5$only