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)=(n!)/(k!(n-k)!)` ways.

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