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?

1 Answer
MeneerNask
Jan 3, 2017

4242 if the order of the other scoops matters, 2121 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 77 choices left.
For the middle scoop she has 66 choices left.
This is a total of 7xx6=427×6=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=2142÷2=21.

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