How many permutations are there of the letters in a word "statistics", such that the word starts with "s" and end with "s".
Is one of the following correct?
$$\frac{10!}{3! \cdot 3! \cdot 1! \cdot 2! \cdot 1!} = 50400$$
or
$$\frac{8!}{1! \cdot 3! \cdot 1! \cdot 2! \cdot 1!} = 3360$$
Best Answer
Think of it like this: $\;s\;x_1\;x_2\;x_3\;x_4\;x_5\;x_6\;x_7\;x_8\;s\;$ with the $x_i$'s come from the set $\{S,t,a,t,i,t,i,c\}$.
This is clearly a permutation of $8$ letters of whom $3$ t's and $2$ i's are redundants. So you have $\dfrac{8!}{2!\times 3!}$ words that starts and ends with $s$.