In an used book store, there are some different mystery novels on a shelf. Suppose there are 64 different ways to buy these novels, including not buying them. How many mystery novels are there on the shelf?
The answer is 6! Does anyone know how to do the question though?? Thanks so much!
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lets say there are \(n\) novels
you could buy none
\(_nC_0=1\) way to do that
you could buy 1
\(_nC_1\) ways to do that
you could buy 2
then you would add them up
when you add, you get \(2^n\)
one way to think of it is adding the entries in the \(n\)th row of pascals triangle gives you \(2^n\)
and since \(2^n=64\) you know \(n=6\)