Question

The number of ways in which $10$ books can be arranged in a row such that two specified books are side by side is

• A. $\frac{10!}{2!}$
• B. $9!$
• C. $9!2!$
• D. $\frac{9!}{2!}$

Answer 1

Answer: (C)

$9!2!$

$\to B_1{B}_2$ can be taken as $1$ block. Now we have $9$ blocks to rearrange.

$B_1{B}_2$

$B_3$

$B_4$

$B_5$

$B_6$

$B_7$

$B_8$

$B_9$

$B_{10}$

No. of ways $=9!$
Additionally, $B_1{B}_2$ can be rearranged in $2!$ ways

Total no. of ways = $2!$ x $9!$