Question

A sportswriter makes his pre-season picks for the top ten teams finish. If there are forty teams, how many different lists could there be?

Answer 1

$\bf _nC_r=\cfrac{n!}{r!(n-r)!}\qquad \begin{cases} n=40\\ r=10 \end{cases}\implies _{40}C_{10}=\cfrac{40!}{10!(40-10)!}$