In the questions below 47 suppose you have 30 books 15 novel

In the questions below (4-7) suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different. In how many ways can you In how many ways can you put the 30 books in a row on a shelf? In how many ways can you get a bunch of four books to give to a friend? In how many ways can you get a bunch of three history books and seven novels to give a friend? In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

Solution

4) The number of ways the books can be arranged is the number of permutations. Which is 30!.

5) You have to give 4 books to a friend. There are 30 books in total. So you have to select only 4. The answer will be 30C4.

6) You have to give 3 history books out of 10 and 7 novels out of 15. So total will be (10C3)X(15C7)

7) Novels are on the left, math are in the middle and history books on the right. So we can rearrange books with in themselves. So the number of ways is (15!)*(5!)*(10!).