Lesson: Calculating Combinations

Comment on Calculating Combinations

Why and how is 0!=1?
gmat-admin's picture

Keep in mind that n! = the product of POSITIVE integers from n to 1. So, 0! doesn't even make any sense, since factorials are only defined for positive integers.

That said, we need to have some agreed-upon convention for dealing with 0! so that we can ensure that calculations involving factorials make sense.

For example, the number of ways to select 3 people from 3 people = 3C3 = 3!/(3!)(0!)

We already know that there is only 1 way to select 3 people from 3 people. So, we need 0! to equal 1. As such, this is an agreed-upon convention.

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