Question

Kara has 10 books on a shelf and decides to move 3 of them to an empty shelf.

In how many different ways can the empty shelf be filled?

The answer is NOT 120, I've already tried that

Answer 1

Answer: 720

Step-by-step explanation: The number of ways to choose 3 books out of 10 is given by the binomial coefficient “10 choose 3” which is equal to 10! / (3! * (10-3)!) = 120. Since the order in which the books are arranged on the shelf matters, for each of these 120 combinations there are 3! = 6 ways to arrange the books on the shelf. Therefore, the total number of ways to fill the empty shelf with 3 books from the original shelf is 120 * 6 = 720.