Question

If ${}^n{P}_5:{}^{n-1}{P}_5=3:2$, find $n$.

Answer 1

${}^n{P}_5{:}^{n-1}{P}_5=3:2$

$\frac{\frac{n!}{(n-5)!}}{\frac{(n-1)!}{(n-6)!}}=\frac{3}{2}$

$\frac{n}{n-5}=\frac{3}{2}$

$2n=3n-15$

$n=15$