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Fundamental Principle of Counting

A shelf conta...

Question

A shelf contains $15$ books, of which $4$ are single volume and the others are $8$ and $3$ volumes respectively. In how many ways can these books be arranged on the shelf so that order of the volumes of same work is maintained $?$

A

4!

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B

8!

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C

3!

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D

4! 8! 3! 3!

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Solution

The correct option is D $4! 8! 3! 3!$
No of books $15$
No of ways $4$ volumes are arranged are $4!$ ways
No of ways $8$ volumes are arranged are $8!$ ways
No of ways $3$ volumes are arranged are $3!$ ways
They are arranged in $3!$ ways one above the other

So no.of ways is $4! 8! 3! 3!$

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