How many ways can 3 novels, 2 math books, and 1 chemistry book be arranged on a bookshelf?

Question by jason m: How many ways can 3 novels, 2 math books, and 1 chemistry book be arranged on a bookshelf?

b) assume the math books must be together and the novels together

c) the novels must be together but the other books can be arranged in any order.




Best answer:

Answer by doug_donaghue
If the math books and novels must be together, then there are 3 'groups' of books and they can be arranged in 3! = 6 ways.
Within each grouping, the math books can be organized in 2! = 2 ways and the novels in 3! = 6 ways. Therefore the total number of ways they can be arranged is 6*2*6 = 72 ways.

If only the novels must be together, then there are 4 groups and they can be arranged in 4! = 24 ways. The group of the novels can still be arranged in 3! = 6 ways so the total number of ways the books can be arranged is 6*24 = 144 ways.

As an aside, if none of the books must be grouped together, there are 6! = 720 ways to arrange them.

Doug

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