Question

Show that the number of six letter words that can be formed using the letters of the word "assist" in which $s^{\prime }s$ alternate with other letters is 12.

Answer 1

The three letters $a\times i\times t\times$ can be arranged in $3!=6$ ways. If the word is to start with any of three letters $a$, n$i$ or $t$ then we have three places marked by $\times$ in which three alikes $s$ can be arranged in
$\frac{3!}{3!}=1$ way. Thus $6\times 1=6$ways
If they are to begin with $s$ then $\times a\times i\times t$ and as above we have again $6\times 1=6$ ways
$\therefore$ Total $=6+6=12$.