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# How many different combinations of 6 numbers are in the numbers 1-15?

I will presume that you are using the space of integers (as there are in infinite number of real or even rational numbers between 1 and 15).

There are 15 integers on the interval of [1,15] and we want to find all possible combinations of 6 numbers from this set.

We use a combination, 6C15= 15! / (6! * (15 - 6)!) = 15! / (6! * 9!)

If you do not have a calculator which does factorials or combinations, then you can do some cancellations to make the computation a little easier:

15! = 15 * 14 * 13 * 12 * 11 * 10 * 9!

so we can cancel the 9!, which leaves us with:

15 * 14 * 13 * 12 * 11 * 10 / 6!

This is still going to involve the multiplication and division of very large numbers, so I took the pansy route and just used a calculator and got:

5,005 different possible combinations. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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