Question

The number of distinct permutation of letters of the word $STATISTICS$ that begin and end with the letter $S$ is

• A. $5040$
• B. $4280$
• C. $3360$
• D. $1680$

Answer 1

Answer: (C)

$3360$

Number of letters in the word $STATISTICS=10$.

We know after fixing two $S^{\prime }s$ $($one in the begining and the other in the end$)$, the number of remaining letters $=10-2=8.$

Since the remaining letters have three $T^{\prime }s$ and two $I^{\prime }s$ therefore, the number of distinct permutations

$=\frac{8!}{3!\times 2!}=\frac{8\times 6\times 5\times 4\times 3}{3\times 2}=3360$