Question

A time traveler can take 3 books with him, and he has 57 books to choose from. How many different ways can the books be selected?

Answer 1

The time traveler can choose 3 books with him, but he can only take 57.

So in this case the order doesn't matter, therefore, we are going to use a combination:

Use the combination formula:

`C\text{ =}(n!)/(r!(n-r)!)`

When n is the total of books and r the sample.

n = 57 and n =3

Replace these values on the formula:

`C=(57!)/(3!(57-3)!)=(57!)/(3!54!)=29260`

Hence, there are 29260 ways that the books can be selected.