Question

Robin has 10 books. Thère is enough space on a shelf for 4 books. In how many ways can 4 of the 10 books bearranged on the shelf?

Answer 1

If the 10 books are all different, we have:

• 10 ways of selecting the first book,

,

• 9 ways of selecting the second book,

,

• 8 ways of selecting the third book,

,

• 7 ways of selecting the fourth book.

The total number of ways to arrange 4 of the 10 books is:

$10\cdot9\cdot8\cdot7=5040.$

Answer

There are 5040 ways of arranging the books.