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Let's say we have 50 numbers (1 - 50). Each data set contains 5 numbers.

How many sets are there, where there are at most x duplicates between two sets. No duplicates within a set are allowed.

Example with less data; Let's say we have 10 numbers: 1,2,3,4,5,6,7,8,9,10 Let's say a set contains 4 numbers.

We want all sets with at most 2 duplicates between two sets.

  • 1,2,3,4
  • 1,2,5,6
  • 1,2,7,8
  • 1,2,9,10
  • 1,3,5,7
  • 1,3,6,8
  • 1,4,5,7
  • etc

I don't even know where to begin with the calculation.

Rick
  • 101
  • When you say two duplicates, do you mean one pair or two pairs? How about a set of three? Which of $(1,1,2,2),(1,1,2,3),(1,1,1,2)$ have two duplicates? None of your examples have any duplicates at all. It would be good to give some that do. – Ross Millikan Feb 10 '20 at 14:15
  • Sorry for the ambiguity. I don't mean duplicates within a set, but duplicates compared to another set. So: (1,2,3,4,5) and (1,2,3,6,7) have 3 duplicates (both have 1,2 and 3) and this is not valid.

    (1,2,3,4,5) and (1,2,6,7,8) only have 2 duplicates (1 and 2) and is valid.

     – Rick Feb 11 '20 at 01:15

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