Eleven books consisting of 5 mathematics, 4 physics and 2 chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books on the same subject are all together is

Question

Smart Achievers · Accepted Answer

(3)

As books of the same subject are to be together, we have 1 + 1 + 1 = 3 groups of books.

So they can be arranged in $3!$ ways. But inside the group, say in Mathematics, 5 individual books can be arranged in $5!$ ways.

Similarly, 4 Physics and 2 Chemistry books can be arranged unit in themselves in $4!$ and $2!$ ways respectively.

$∴$ Total number of ways $= 5! \times 4! \times 3! \times 2!$

Solution

Q.
Eleven books consisting of 5 mathematics, 4 physics and 2 chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books on the same subject are all together is

1 $4! 2!$

2 $11!$

3 $5! 4! 3! 2!$

4 none of these

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Solution

Q. Eleven books consisting of 5 mathematics, 4 physics and 2 chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books on the same subject are all together is

1 4! 2!

2 11!