Question

Eleven books consisting of $5$ Mathematics, $4$ Physics and $2$ on Chemistry are placed on a shelf at random. Find the number of possible ways of arranging them on the assumption that the books on the same subject are all together.

Answer 1

Here,

Total number of books $=5+4+2=11$

Now,

$11$ books can be arranged in $11!$ ways.

Now, if we want to keep same subject's books together, then number of ways of arranging them subject wise $=3!$

Further,

$5$ Mathematics books can be arranged in $5!$ ways

$4$ Physics books can be arranged in $4!$ ways

$2$ Chemistry books can be arranged in $2!$ ways

Therefore,

Total number of desired event $=2!\times 3!\times 4!\times 5!$

Therefore,

Required probability $=\frac{2!\times 3!\times 4!\times 5!}{11!}$