[Math] 8-digit sequences invoving exactly 6 different digits

combinatorics

How many 8-digit sequences are there involving exactly six different digits? How can I approach this problem?

Best Answer

HINT:

  • Count the ways to choose a set of $6$ digits to use.
  • Given a set of $6$ digits, either you use one digit $3$ times, or you use two digits twice each. Treat those cases separately.
  • In each case you must first choose the digit(s) to be duplicated; in how many ways can that be done? Then you’re solving a problem of the same general type as counting the number of distinguishable arrangements of the letters in the name MISSISSIPPI; I expect that you’ve done some problems of that type.
  • Properly combine the results of the previous steps.
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