Q&A

# Explain to a 9 year old — To count each possibility c times, why divide by c? Why not subtract by c?

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Please see the embolded phrase below. How can you explain to a 9 year old why you

1. must divide by $c$?

2. can't subtract by $c$?

In many counting problems, it is not easy to directly count each possibility once and only once. If, however, we are able to count each possibility exactly c times for some c, then we can adjust by dividing by $c$. For example, if we have exactly double-counted each possibility, we can divide by 2 to get the correct count. We call this adjusting for overcounting.

Blitzstein. Introduction to Probability (2019 2 ed). pp. 14-15.

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