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 3 toppings?

Answer 1

Ok, so:

Let's say you have 5 cheeses A,B,C,D and E.

You want to make a combination of 2 cheeses.

These are the possible combinations.

AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.

So, there are 10 possibilities to make a combination of 2 cheeses.

Now, we also have 10C3 choices of toppings. Because, we have a combination of 10 different toppings and 3 topping to choose.

Now, remember that:

In this case, we have n = 10 and r = 3.

If we replace in the equation, we obtain 10C3 = 120.

So, there are 120 possibilities to make a combination of 3 toppings.

Finally, we multiply the possibilities we found before.

120 * 10 = 1200

Therefore, a pizza can be made with 2 cheese and 3 toppings in 1200 ways.