Practise Calculating the Number of Different Combinations

Combinations appear regularly in everyday life.

If we know how many total combinations, we can also look for probability. 

 

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

 

Example

 

 

At Jack's school there are some uniform choices:

short sleeve T-shirt, short sleeve shirt, long sleeve shirt

grey trousers, grey shorts

jumper, blazer

 

How many different combinations are there?

 

Answer

There are 3 top options

There are 2 bottom options

There are 2 jumper options

 

So there are 3 x 2 x 2 = 12 possible combinations

 

Probability

We could also be asked, what is the probability of a boy choosing to wear a short sleeve t-shirt, grey shorts and a jumper?

As there is only one outcome that matches this combination we could write the probability as 1/12

 

Does that make sense?

 

 

Let's have a go at some questions.