What to Do When One Gets Two Different Answers to a Counting Problem

This short article narrates a real-life classroom episode: a situation where two different answers were obtained to a counting problem and the class was nonplussed for a while. Ultimately, good sense prevailed and we were able to discover the error.

The problem studied was this:

Eight tennis players wish to split up into four pairs to play four singles games. In how many ways can they do this?

Note that the pairs do not have any identifying names; it does not matter which pair plays on which court. What is of interest is only who gets paired with whom, and in how many different ways this pairing can be done. We present three different approaches, just as it happened in the classroom.

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