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There is a class of 20, and we are going to pick a team of three people at random, and we want to know:

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## Answers

### This Is a Certified Answer

If n is the size of the larger collection, and r is the number of elements that will be selected, then the number of combinations is given by

In the question just posed, n = 20, r = 3, and n – r = 17. Therefore

To simplify this, consider that:

20 = (20)(19)(18)(17)

That neat little trick allow us to enormously simplify the combinations formula:

= 1140

### This Is a Certified Answer

If n is the size of the larger collection, and r is the number of elements that will be selected, then the number of combinations is given by

# of combinations =

In the question just posed, n = 20, r = 3, and n – r = 17. Therefore,

# of combinations =

To simplify this, consider that:

20! = (20)(19)(18)(17)(the product of all the numbers less than 17)

Or, in other words,

20! = (20)(19)(18)(17!)

That neat little trick allow us to enormously simplify the combinations formula:

# of combinations = = 1140