Question

If all $S$ come together, then in how many ways the letters of the word $SUCCESSFUL$ be arranged?

Answer 1

$SUCCESSFUL$ is a $10$ letter word.

In this word letter $S$ repeat three times, and letter $C$ repeat two times.

In this problem one condition is that all $S$ come together.

For solving this problem, we have to consider three $S$ together treated as one digit.

So now we are considering a $9$ letter word.

$\therefore$ number of ways the $9$ letters of the word $successful$ be arranged in $9!$ ways.

But here the letter $C$ is repeating $2$ times. We have to divide the result by $2!$

Number of ways $SUCCESSFUL$ can be arranged $=\frac{9!}{2!}=\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2!}{2!}=181440$ ways