Question

If Jacob owns 12 books, how many different ways can he arrange 3 of these books on a single bookshelf

Answer 1

1320

Explanation:

We will think as follows. Recall that at first, he chooses 3 books. Then, we want to see in how many ways he can arrange this books. For the first book, he has 3 options, for the second one 2 and for the third 1. Then, the total number of ways in which he can arrange 3 books is 3!. So we know that after choosing 3 books, he can arrange them in 3! ways. So, we want to check the total number of ways he can choose 3 books out of 12. That is given by the binomial coefficient
`\binom{12}{3}`. Then, the total number of ways of arranging 3 books is

`\binom{12}{3}\cdot 3! = (12!)/((12-3)! 3!)\cdot 3! =   (12!)/((12-3)!) = 1320`

Thus, he can arrange 3 books out of 12 in 1320 different ways