Everything to learn better...

Home

Maths

Probability

Listing outcomes

Listing outcomes

Select Lesson

Proportion


Ratio


Explainer Video

Loading...
Tutor: Alice

Summary

Listing outcomes

In a nutshell

To find the probabilities of outcomes in an experiment, you need to know how many different outcomes there are. In some cases, you may have to list all possible outcomes, and in other situations you can use the multiplication principle to work out how many there are.



​​Combinations

You can use combinations to find the total number of possible events of an experiment.


Example 1

Nina bought 33​ different cake mixes: chocolate, strawberry and lemon. She also bought chocolate chips and pink hearts to decorate them, and for any cake she must have 11​ mix and 11 decoration. The combinations she can make can be listed as follows:


  1. Chocolate mix with chocolate chips
  2. Strawberry mix with chocolate chips
  3. Lemon mix with chocolate chips
  4. Chocolate mix with pink hearts
  5. Strawberry mix with pink hearts
  6. Lemon mix with pink hearts

Tip: Do your best to list the options in a logical order, so you don't miss one by accident!



Listing possible combinations

​​Procedure

1.
Make a table where the column headings detail the different options (for the cake example this is 22: the cake mix and the decoration).
2.
Fill in the table with a combination of options, writing the relevant option in the correct column.
3.
Repeat until all combinations are listed.


Example 2

Nina can list the possible combinations of her cakes in the following table:


Number

Cake Decoration

Cake Mix

11
Chocolate chips
Chocolate
22
Chocolate chips
Strawberry
33
Chocolate chips
Lemon
44
Pink hearts
Chocolate
55
Pink hearts
Strawberry
66
Pink hearts
Lemon



Number of combinations

It is possible to calculate the number of possible combinations without listing them all.


Procedure

1.
Look at the different aspects of each combination available.
2.
Determine the number of choices for each aspect.
3.
Multiply the number of choices for every aspect together


Example 3

Luke has 33​ pairs of trousers, 44​ shirts and 22​ pairs of shoes. How many different outfits can he wear?


Total combinations: Number of trousers ×\times Number of shirts  ×\times  Number of shoes 

3×4×2=243\times4\times2 = \underline{24}

Create an account to read the summary

Exercises

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What are examples of combinations?

How do you work out how many combinations there are without listing them all?

Is repetition allowed in combinations?

Beta

I'm Vulpy, your AI study buddy! Let's study together.