Question

Can someone please explain to me how to do this:

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

Oooh, these are fun! Think in terms of "choices" and "slots."

[Cheese]
For cheese we have two slots to fill:
___ ___
For our first slot, we have 5 different cheeses to choose from,
_5_ ___
For our second slot, we only have 4 cheeses left to choose from (I'm assuming we didn't pick the same cheese),
_5_ _4_
The total number of cheese options is 5*4 = 20.

[Toppings]
For toppings we have 4 slots to fill:
___ ___ ___ ___
For the first slot, we have 10 choices,
_10_ ___ ___ ___
For the second, 9 choices,
_10_ _9_ ___ ___
And so on,for the third and fourth slot,
_10_ _9_ _8_ _7_
The total number of topping options is 10*9*8*7 = 5040.

[All together]
We have 20 cheese options, and 5040 topping options. For every cheese option, we have 5040 topping options. To get the grand total, multiply:
20*5040 = 100,800 ways in total!