# There are six different books distributed to 3 boys. Each boy at least got one book. How many ways of the combinations?

##### 1 Answer

Nov 25, 2017

1920

#### Explanation:

There are a few cases we need to explore:

- If each boy gets only 1 book each (
**3 books total**), we can set up a permutation (order matters):

- If each boy gets 2 books each (
**6 books total**), we can set up a permutation:

- If one boy gets 2 books and the others get 1 each (
**4 books total**), we can set up a permutation expression that starts with each boy getting one book, and then the remaining 4th book can go to any one of the three boys:

- If two boys gets 2 books and the other gets 1 (
**5 books total**), we can set up a permutation expression that starts with each boy getting one book, and then the remaining 4th and 5th books can go to any two of the three boys:

And now we add up the cases: