Question

The number of ways in which the letters of the word "SUCCESSFUL" be arranged such that The 'S's and 'U's will come together is

• A. $7!$
• B. $\frac{7!}{2!}$
• C. $\frac{7!}{2!2!}$
• D. $\frac{7!}{2!2!2!}$

Answer 1

Answer: (B)

$\frac{7!}{2!}$

Considering all S's as a pack, and all the U's as a pack
$\left[SSS\right]\left[UU\right]CCEFl$
Hence 7 objects ...(since all the S's form a single pack and all the U's form a single pack, therefore we consider the entire pack as one object)
Now C is repeated twice.
Therefore the question reduces to, number of ways of arranging 7 objects where an object is repeated twice.
Hence the required permutation will be
$=\frac{7!}{2!}$