Counting combinations
You learn to work out the number of possible combinations from two groups by multiplying.
How to work it out
Are you choosing one from each of two groups? Then multiply the numbers of choices together.
3 × 4
A worked example
3 soups and 4 rolls
- Look at how many choices the first group has: 3 kinds of soup.
- Look at the second group: 4 kinds of roll.
- Multiply the numbers: 3 × 4 = 12.
- There are 12 possible combinations.
More examples
2 shirts and 5 pairs of trousers
- Multiply the choices: 2 × 5 = 10.
- There are 10 possible combinations.
4 ice-cream flavours and 3 toppings
- Multiply the choices: 4 × 3 = 12.
- There are 12 possible combinations.
Try it yourself
Multiply the number of choices from both groups
You can choose from 4 starters and 5 main courses. You pick one of each. How many combinations are possible?
Multiply the number of choices from both groups
You can choose from 3 shirts and 6 pairs of trousers. You pick one of each. How many combinations are possible?
Watch out
You add the choices instead of multiplying: 3 + 4 = 7.
With each soup you can choose each roll: that is repeated adding, so multiply.
Tips
- Number of options group 1 times number of options group 2 gives the total number of combinations.
Why it works
When you make a choice from two groups, you combine every option from group 1 with every option from group 2. By multiplying the numbers, you instantly know how many combinations there are.