SOLUTION: The Creamery serves dishes of frozen yogurt, and a customer may choose from 7 different toppings. How many ways can a customer choose a dish of yogurt with up to 3 different toppi

Question 602204: The Creamery serves dishes of frozen yogurt, and a customer may choose from 7 different toppings. How many ways can a customer choose a dish of yogurt with up to 3 different toppings, including the choice of no tipping?
{I think this is a combination, or C(n,r), but does not provide the correct answer. That answer is: 64, however, I don't know how to correctly work it out. Help is appreciated!
DC
Answer by jim_thompson5910(28504) (Show Source):
You can put this solution on YOUR website!
The key word "up to" means everything below that value and that value is included. So "up to 3 toppings" means you can choose 0, 1, 2, or 3 toppings.

There are C(7,3) = 35 ways to choose 3 toppings

There are C(7,2) = 21 ways to choose 2 toppings

There are C(7,1) = 7 ways to choose 1 topping

and finally, there is only one way to choose no toppings

So overall, there are 35+21+7+1 = 64 different ways to choose up to 3 toppings.

Note: C(n,r) = (n!)/(r!(n-r)!). So for example, C(7,3) = (7!)/(3!(7-3)!) = 35