Question

A colour palette at a paint store has 6 shades of blue. Kelsie is choosing 2 shades of blue to paint her room. How many pairs of colours can she pick from the colour palette?

A.) 12
B.) 15
C.) 30
D.) 720

Answer 1

B.) 15

Explanation:

The order in which the shades are chosen is not important. For example, choosing powder then sky is the same outcome as choosing sky then powder. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

2 shades from a set of 6. So

`C_(6,2) = (6!)/(2!(6-2)!) = 15`

So the correct answer is:

B.) 15