# How many ways can you make a sandwich by choosing 4 out of 10 ingredients?

##### 2 Answers

#### Explanation:

While there is a formula to use, it is quite easy to think through the question as follows:

When we choose the first ingredient, there are 10 choices.

When we now choose the second ingredient there are 9 choices.

For the third, there are 8.

For the fourth there are 7.

Each ingredient can be combined with the others, giving:

That's a lot of choices!

If the order does not matter 210

That is: cheese and tomato is the same as tomato and cheese

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If the order does matter 5040

#### Explanation:

Sometimes you will see factorial written as

So

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Depends on how you wish to consider the paring up.

This can be written as

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This can be written as