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A 5-digit combination can be obtained as:

  • five 1-digit numbers from 1-9,
  • three 1-digit numbers from 1-9 and one 2-digit number from 10-39, or
  • one 1-digit number from 1-9 and two 2-digit numbers from 10-39.

There are 9C5 = 126 of the first kind,

9C3*30C1 = 84*30 = 2520 of the second, and 9C1*30C2 = 9*435 = 3915 of the third.

All together, there are 126 + 2520 + 3915 = 6561 5-digit combinations.

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Q: How many 5 digit combinations can be made from 1 to 39 digits?
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