Question

Ladonna has 7 books to place on a shelf. How many possible arrangements of all 7 books are there?

Answer 1

Given:

The number of books is 7.

The arrangements of 7 books are,

`\begin{gathered} ^nP_r=(n!)/((n-r)!) \\ n=7,r=7 \end{gathered}`

It gives,

`\begin{gathered} ^7P_7=(7!)/((7-7)!) \\ =(7!)/(0!) \\ =(7!)/(1) \\ =7! \\ =1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7 \\ =5040 \end{gathered}`

Answer: number of ways are 5040.