An ice cream shop offers 6 kinds of ice cream. What is the greatest number of two scoop sundaes that can be made such that each sundae contains two types of ice cream and no two sundaes are the same combination?

20

Step-by-step explanation:

Let’s label the ice-creams first so we can avoid confusion.

1, 2, 3, 4, 5, 6

so we have to remember to make as many combinations as possible without repeating the same combination and we can’t have two scoops with the same ice cream either. All of the possible combos are below and none of them repeat and they don’t have the same type of ice cream in two scoops.

1-2

1-3

1-4

1-5

1-6

2-2

2-3

2-4

2-5

2-6

3-3

3-4

3-5

3-6

4-4

4-5

4-6

5-5

5-6

6-5