Question

Anna goes to a frozen yogurt shop. She can choose from any of the following toppings: peanuts, caramel sauce, butterscotch chips, strawberries, and cookie dough bits. How many different variations of yogurt and toppings can be made?

Answer 1

Answer:

32 variations

Step-by-step explanation:

Anna can choose any number from 0 to 5 different toppings, which is the sum of the combinations of 0 out of 5, 1 out of 5, 2 out of 5, 3 out of 5, 4 out of 5 and 5, out of 5. The number of different variations is:

$n = \frac{5!}{(5-0)!0!} + \frac{5!}{(5-1)!1!}+ \frac{5!}{(5-2)!2!} +\frac{5!}{(5-3)!3!} +\frac{5!}{(5-4)!4!} +\frac{5!}{(5-5)!5!}\\ n=1+5+10+10+5+1\\n=32$

There are 32 different variations of yogurt and toppings.