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

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=(15!)/((15-7)!) \\ \\ Number\text{ }Of\text{ }Ways=(15!)/(8!) \\ \\ Number\text{ }Of\text{ }Ways=(15*14*13*12*11*10*9*8!)/(8!) \\ \\ Number\text{ }Of\text{ }Ways=32432400 \end{gathered}`

Therefore, the answer is

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