Answer
$10,987,286,400$
Work Step by Step
Use the formula $P(n,r)=\dfrac{n!}{(n-r)!}$.
Here, we have $n=15$ and $r=10$ so substitute these values into the formula: above to obtain:
$P(15,10)=\dfrac{15!}{(15-10)!}\\\\
P(15,10)=\dfrac{15!}{5!}\\\\
P(15,10)=\dfrac{15{\times}14{\times}13{\times}12{\times}11{\times}10{\times}9{\times}8{\times}7{\times}6{\times}5{\times}4{\times}3{\times}2{\times}1}{5{\times}4{\times}3{\times}2{\times}1}$
Cancel out common factors to get:
$P(15,10)=15\times14\times13\times12\times11\times10\times9\times8\times7\times6 \\
P(15,10)=10,987,286,400$
