SOLUTION: There are 8 physics textbooks, 7 us history textbooks, 4 calculus textbooks, and 3 resource books on a shelf. Assuming the books in each category are DISTINCT how many ways can th

Question 190794: There are 8 physics textbooks, 7 us history textbooks, 4 calculus textbooks, and 3 resource books on a shelf. Assuming the books in each category are DISTINCT how many ways can they be arranged if books of the same kind must be together?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let's just look at the Physics books first. There are 8 of them. There are 8 ways to choose the first one, and then 7 ways to choose the second one, so there are 8 times 7 = 56 ways to choose the first two...and so on. So there are

ways to arrange the Physics books.

Likewise, there are 7! ways to arrange the History books, 4! ways to arrange the Calculus books, and 3! ways to arrange the resource books, and finally, there are 4 groups of books, so there are 4! ways to arrange the groups. Putting it all together,

The built-in Windows calculator has an n! button, but that's all the help I'm going to give you on the arithmetic for this one.

John

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