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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.

Add these together.

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Q: How many different 6 digit combinations can be made from 10 numbers if you can repeat a number?
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How many combinations of six numbers can be had from seven numbers?

The number of combinations of six numbers that can be made from seven numbers will depend on if you can repeat numbers. In all there are over 2,000 different numbers that can be made.


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