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Question
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
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Solution
First we take books of a particular subject as one unit.
Thus there are 4 units which can be arranged in 4! = 24 ways.
Now in each of arrangements
Mathematics books can be arranged in 3! ways,
History books in 4! ways,
Chemistry books in 3! ways
And biology books in 2! ways.
Thus the total number of ways = 4! × 3! × 4! × 3! × 2! = 41472.
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