Question

A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 4 toppings?

Answer 1

The order doesn't matter.

$k$ objects can be chosen out of $n$ objects, when the order doesn't matter, in $C(n,k)=\dfrac{n!}{k!(n-k)!}$ ways.

So, the answer is $C(5,2)\cdot C(10,4)=\dfrac{5!}{2!3!}\cdot\dfrac{10!}{4!6!}=\dfrac{4\cdot5}{2}\cdot\dfrac{7\cdot8\cdot9\cdot10}{2\cdot3\cdot4}=2,100$ ways.