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
Jan 3, 2017

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


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: