Explain to a 9 year old — To count each possibility c times, why divide by c? Why not subtract by c?
Please see the embolded phrase below. How can you explain to a 9 year old why you
must divide by $c$?
can't subtract by $c$?
1.4.2 Adjusting for overcounting
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.