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. $34,560$
• B. $34,500$
• C. $31,540$
• D. $32,850$

Answer 1

The correct option is A $34,560$

Books on each subject can be arranged amongst themselves in the following ways:

Mathematics-$5$ books in $P(5,5)$ ways$=5!$ways

Physics-$4$ books in $P(4,4)$ ways$=4!$ways

Chemistry-$2$ books in $P(2,2)$ ways$=2!$ways

Since, the arrangement of these three groups of subjects can be made in $P(3,3)$ 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