Question

An ice cream parlour has 8 flavours of ice cream. Joyce wants a cone with 3 different scoops. She wants chocolate mint on the top. How many different ways can she choose the other 2 flavours?

Answer 1

`42` if the order of the other scoops matters, `21` if it doesn't.

Explanation:

Since the top scoop is already defined, we only deal with the middle and bottom scoop.

For the bottom scoop she has `7` choices left.
For the middle scoop she has `6` choices left.
This is a total of `7xx6=42` permutations .

If the order doen't matter, then every of the above choices has a double in reversed order. So the number of combinations is:
`42div2=21`.