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# How many different 6 digit combinations can be made from 10 numbers if you can repeat a number?

There are just 5,005.

• There are 10C6 = 210 combinations with 6 different numbers.
• There are 10C5 = 252 combinations with 5 different numbers. One of these needs to be duplicated and the one to be duplicated can be chosen in 5 ways so there are 1260 of these.
• There are 10C4 = 210 combinations with 4 different numbers. Either one of them appears three times or two are doubled. That can be done in 10 ways so there are 2,100 of these.
• There are 10C3 = 120 combinations with 3 different numbers. Either one of them appears 4 times, or one twice and another three times, or all three appear twice. That can be done in 10 ways so there are 1,200 of these.
• There are 10C2 = 45 combinations with 2 different numbers. Either one of them appears 5 times, or one twice and another four times, or both three times. That can be done in 5 ways so there are 225 of these.
• There are 10C1 = 10 combinations with just 1 number repeated six times. 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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