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

Question

anonymous · Answer

We have three things to choose: the first dip, the second dip and the topping. 

For the first dip we have 10 choices.
For the second dip we have 10 choices (since it says we can use the same flavor again.)
For the topping we have 15 choices.

The total number of combinations is: $$10 \times 10 \times 15 = 1500$$

You can picture this as a tree diagram:
|dw:1394474448423:dw|

If you drew out all the possibilities and counted them you would get 1500.