Question

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 of the same subject are all together is?

• A. $4!2!$
• B. $11!$
• C. $5!4!3!2!$
• D. None of these

Answer 1

The correct option is D

None of these

Given:

Number of Mathematics books $=5$

Number of Physics books $=4$

Number of Chemistry books $=2$

According to the question,

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

$=11$

$\therefore$ Total number of ways in which $11$ books can be arranged $=11!$

Now, the number of ways of arrangement in which same subject's book be together $=3!$

Also,

Number of ways in which Mathematics book can be arranged $=5!$

Number of ways in which Physics book can be arranged $=4!$

Number of ways in which Chemistry book can be arranged $=2!$

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

So, the Required probability $=\frac{\mathbf{2}\mathbf{!}\mathbf{\times }\mathbf{3}\mathbf{!}\mathbf{\times }\mathbf{4}\mathbf{!}\mathbf{\times }\mathbf{5}\mathbf{!}}{\mathbf{11}\mathbf{!}}$

Hence, Option ‘D’ is Correct.