Question

How many ways can we arrange five of the seven Harry Potter books on a shelf if Harry Potter and The Chamber of Secrets must be one of them?

Answer 1

There are 7 Harry potter books and 5 books needs to be arranged.

One of the five place is filled by book "Harry Potter and The Chamber of Secrets" and remaining 4 places must be filled by remaining 6 books.

So number of ways are,

`\begin{gathered} 1\cdot^6P_4=1\cdot(6!)/((6-4)!) \\ =1\cdot(6\cdot5\cdot4\cdot3\cdot2\cdot1)/(2\cdot1) \\ =1\cdot6\cdot5\cdot4\cdot3 \\ =360 \end{gathered}`

So there are 360 ways in which 5 of 7 Harry pooter book can be arranges such that " Harry Potter and The Chamber of Secrets" must included.