binomial coefficient

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from the PRMO and some from the AIME (the ‘American Invitational Mathematics Examination’). As usual, we pose the problems first and present the solutions later.

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?

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