A combination is a way of selecting something out of all the different options where the order doesn't matter.

To work out the total number of combinations, we can multiply together the numbers of different options.

Example

Jack goes to buy an Italian ice cream.

He can choose from a small cone, a medium cone or a large cone. 

There are 30 flavours. 

He can have his ice cream with a wafer or without.

How many different combinations are there?

Answer

There are 3 sizes.

There are 30 flavours.

That means that, so far, there are 3 x 30 = 90 different combinations.

There are 2 options for the wafer (with or without).

So there are now 3 x 30 x 2 = 180 combinations.

That's a lot of different combinations - if you had a different one every day, it would still take you six months before you'd have had them all!

It might not be such a good food choice though - ice cream might well be delicious but eating one every day could lead to some health issues!

Let's have a go at some questions now.