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

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

The combination is given by
$_6C_2=\frac{6!}{2!4!}=\frac{720}{48}=15$

Answer 2

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 $C(n,k)=\dfrac{n!}{k!(n-k)!}$ ways.

So, the answer is $C(6,2)=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15$ ways.