Question

The number of ways in which $6$ Telugu, $4$ Hindi and $3$ English books be placed in a row on a shelf so that the books of the same subject should remain together is

• A. $6!4!3!$
• B. $3!6!4!3!$
• C. $\frac{13!}{6!4!3!}$
• D. $\frac{13!}{6!4!3!3!}$

Answer 1

Answer: (B)

Now, we make three blocks, one each for each language

$\left\{T_1{T}_2{T}_3{T}_4{T}_5{T}_6\right\}$, $\left\{E_1{E}_2{E}_3\right\}$, $\left\{H_1{H}_2{H}_3{H}_4\right\}$

Clearly,

The number of ways in which these $3$ blocks can be rearranged is $3!$ ways. ---(1)

Number of ways in which the Telugu books can be rearranged among themselves $=6!$ ---(2)

Number of ways in which the Hindi books can be rearranged among themselves $=4!$ ---(3)

Number of ways in which the Hindi books can be rearranged among themselves $=3!$ ---(4)

From (1), (2), (3) and (4)

So, the total number of of ways $=3!6!4!3!$

Hence, Option B is correct.