Question

A frozen yogurt shop offers 10 different flavors of yogurt and 15 different toppings. How many double-dip sundae combinations can be created with 1 topping? One yogurt flavor may be used for both dips.

Answer 1

Answer:

825

Step-by-step explanation:

To count how many different double-dip sundae combinations exist, we can count first how many combinations exist where the same yogurt flavor is used for both dips, and then count how many combinations exists where different yogurt flavors are used for the two dips, and simply add them together.

Type 1 - Both dips are of the same flavor: In this case we can choose 10 different flavors for our dips flavor, and for EACH of those 10 choices, we have 15 available options for which topping to choose. So the total sundaes of this kind are 10*15=150.

Type 2 - Dips are of the different flavor: In this case we have to choose 2 different flavors for our dips, and we have 10 available flavors for them. So we have to pick 2 flavors out of 10, which can be done in ${10 \choose 2}=45$ ways. Now, for EACH of those choices, we can pick 15 different toppings, so the total sundaes of this kind are 45*15=675.

Therefore the total number of different sundae combinations that we can choose is 150+675=825.

Answer 2

25 yogurt dips 
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