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#1: Initial revision by user avatar DNB‭ · 2021-07-09T04:33:28Z (over 3 years ago)
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

1.  must divide by $c$? 

2. 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.