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Question

The number of ways in which $$5$$ Mathematics, $$4$$ Physics, $$2$$ Chemistry books can be arranged in a shelf if the books on the same subject are kept together.


A
34,560
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B
34,500
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C
31,540
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D
32,850
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Solution

The correct option is A $$34,560$$
Books on each subject can be arranged amongst themselves in the following ways:
Mathematics-$$5$$ books in $$P\left(5,5\right)$$ ways$$=5!$$ways
Physics-$$4$$ books in $$P\left(4,4\right)$$ ways$$=4!$$ways
Chemistry-$$2$$ books in $$P\left(2,2\right)$$ ways$$=2!$$ways
Since, the arrangement of these three groups of subjects can be made in $$P\left(3,3\right)$$ ways.
By the multiplication principle, the required number of permutations are 
$$5!\times 4!\times 2!\times 3!=120\times 24\times 2\times 6=34,560$$ ways


Mathematics

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