Question

The student body president needs to assign each officially sanctioned club on campus a unique ID code for purposes of tracking expenses and activities. She decides to use the letters

A, B, and C to create a unique three-character code for each club.
How many clubs can be assigned a unique ID code according to this proposal?

Answer 1

6

Explanation:

There are 6 permutations of the 3 letters:

ABC, ACB, BAC, BCA, CAB, CBA

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Comment on the proposal

It seems like there might be more than 6 clubs on campus. There would be 24 possible 3-letter codes drawn from a group of 4 letters, and 60 possible 3-letter codes drawn from a group of 5 letters.

Transposition of letters is a common error when reading or copying such code groups. This seems like it could result in an accounting nightmare as expenses got mixed up between clubs.

The proposal might want to consider schemes that would be less error-prone, such as using combinations of letters that would permit them to always be in alphabetical (or reverse alphabetical) order. Using 3-letter codes from a group of 5 letters, with codes being in only alphabetical or reverse alphabetical order would give 20 possible codes and a much lower error probability.