Question

Anne needs 2 kinds of fruits to prepare a fruit salad. She has 6 kinds of fruits to choose from. In how many ways can she choose the fruits? Identify if the situation involves combinations or permutations.

Answer 1

The order doesn't matter. It's the combination then.

`k` objects can be chosen out of
`n` objects, when the order doesn't matter, in
`C(n,k)=(n!)/(k!(n-k)!)` ways.

So, the answer is
`C(6,2)=(6!)/(2!4!)=(5\cdot6)/(2)=15` ways.

Answer 2

There are 15 ways she can choose the fruits. Since order is not important, this is a combination.

The combination is given by

`_6C_2=(6!)/(2!4!)=(720)/(48)=15`