Question 1178850: Six math books, five science books, and two English books are to be arranged on a shelf, so that books of the same subject must be together. How many ways can this be done? *
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Six math books, five science books, and two English books are to be arranged on a shelf, so that books of the same subject must be together. How many ways can this be done? *
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Math books: 6! ways to arrange them
Science books: 5! ways to arrange them
English books: 2! ways to arrange them
6!*5!*2! = 720*120*2 = 172800 ways to arrange the Math, Science, and English books together, in that particular subject order.
You can also arrange the three subjects in 3! ways, bringing the total number of arrangements to:
(172800)*3! = 172800*6 =  ways
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