Question

How many ways can you arrange books on a shelf if you have 15 books to choose from, but you only have enough room for 7 books on the shelf?

Answer 1

Solution

Since we want to to arrange, we have to use permutation

$\begin{gathered} Number\text{ }Of\text{ }Ways=P(15,7) \\ \\ Number\text{ }Of\text{ }Ways=\frac{15!}{(15-7)!} \\ \\ Number\text{ }Of\text{ }Ways=\frac{15!}{8!} \\ \\ Number\text{ }Of\text{ }Ways=\frac{15\times14\times13\times12\times11\times10\times9\times8!}{8!} \\ \\ Number\text{ }Of\text{ }Ways=32432400 \end{gathered}$

Therefore, the answer is

$\begin{equation*} 32432400 \end{equation*}$