# 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?

Jan 3, 2017

$42$ 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 $7 \times 6 = 42$ 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:
$42 \div 2 = 21$.