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Listing outcomes

Listing outcomes

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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 333​ 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 111​ mix and 111 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 222: 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

111​
Chocolate chips
Chocolate
222​
Chocolate chips
Strawberry
333​
Chocolate chips
Lemon
444​
Pink hearts
Chocolate
555​
Pink hearts
Strawberry
666​
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 333​ pairs of trousers, 444​ shirts and 222​ 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=24‾3\times4\times2 = \underline{24}3×4×2=24​

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Calculating probability

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Calculating probability

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Listing outcomes

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Listing outcomes

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FAQs - Frequently Asked Questions

What are examples of combinations?

Examples include picking teams of 3 from a group of 10 people, or choosing 2 ice cream flavours from 5 at a restaurant.

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

Identify how many of each "choice" there are, then multiply the number of choices for every aspect together.

Is repetition allowed in combinations?

No, repetition is not allowed in combinations. Two combinations are still the same even if the order of the aspects is listed differently.

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