contestada

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?

Respuesta :

konrad509

The order doesn't matter.

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

So, the answer is [tex] 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 [/tex] ways.