CMAT Exam 2023 Shift 2 Solved Paper

Total number of 8 -letter words possible using letters $\mathit{S},\mathit{Y},\mathit{L},\mathit{L},\mathit{A},\mathit{B},\mathit{U},\mathit{S}$ is $\frac{8!}{2!2!}$
Statement I:
We can find total number of 8 -letter words by considering 2 S's as a single unit and arranging 7 units, i.e. (SS), Y, $\mathit{L},\mathit{L},\mathit{A},\mathit{B},\mathit{U}$
Total number of ways $=\frac{7!}{2!}$
Required probability $\frac{\frac{7!}{2!}}{\frac{8!}{2!2!}}=\frac{2}{8}=\frac{1}{4}$
Therefore, statement $\mathit{I}$ is correct.
Statement II:
We can find total number of 8-letter words such that L's are at ends by arranging remaining 6 letters in the middle.
Total number of ways $=\frac{6!}{2!}$
Required probability $=\frac{\frac{6!}{2!}}{\frac{8!}{2!2!}}=\frac{2}{56}=\frac{1}{28}$
Therefore, statement II is correct.
The answer is option A.