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Added clarification for a common mistake
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SherTheCoder authored and fifthist committed Apr 8, 2024
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7 changes: 6 additions & 1 deletion src/chapters/1/sections/counting/problems/14.tex
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is $4 * 256 = 1024$.

We wish to sample two pizzas, with replacement, out of the $1024$ possibilities.
By Einstein-Bose, there are a total of $\binom{1025}{2}$ choices.
By Einstein-Bose, there are a total of $\binom{1025}{2}$ choices.

A common mistake is to use multiplication rule to get $(2^8)*(2^8)$ as
total possible combinations for two pizzas, and try to adjust for overcounting
by dividing the result with 2 (as order between pizzas doesn't matter). This
fails because the possibilities with identical pizzas are counted only once.

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