Question

A time traveler can take 4 books with him, and he has 73 books to choose from. How many different ways can the books be selected?

Answer 1

`1,088,430`

Step-by-step explanation

We want to find the number of ways that the books can be selected.

To do this, we have to find the combination of 73 and 4. That is:

`^(73)C_4`

Simplifying, we have:

`\begin{gathered} ^(73)C_4=(73!)/((73-4)!4!) \\ \Rightarrow(73!)/(69!4!)=(73\cdot72\cdot71\cdot70\cdot69!)/(69!\cdot4!) \\ \Rightarrow(73\cdot72\cdot71\cdot70)/(4\cdot3\cdot2\cdot1) \\ \Rightarrow1,088,430 \end{gathered}`

That is the number of ways that the books can be selected.