Question

A pizza place offers 6 different cheeses and 12 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?

Answer 1

If the order of the toppings does not matter the number of combinations of toppings is
\[12C3=\frac{12!}{3!9!}=\frac{12\times 11\times 10}{3\times 2}\]
Each combination of toppings can be had with a choice of 6 different cheese.
The number of different ways of making a pizza is
\[\frac{6\times 12\times 11\times 10}{3\times 2}\]