Suppose we have 4 books on Math, 5 books on English and 6 books on History. In how many ways you can put them on your bookshelf if you want

1) The first book is a math book.

2) All math books are at the beginning.

3) Math and English books will stay together.

4) The first book and the last book are both Math books.

(I'm completely lost with this problem. If someone can give me an explanation that would be great.)

I know that we have 3 subjects so there are 3! Or 6 possibilities and for 4 math books we have 4! or 24 ways to order. When it is 5 English books we have 5! or 120 ways to order. If it is 6 history books we have 6! Or 720 ways to order. So I think the answer is 6∗24∗120∗720=

12,441,600 ways to order the books .

primedepot333 Nov 4, 2020