Permutations and Combinations

In how many ways can the letters of the word $SUCCESS$ be arranged so that all $Ss$ are together?


The word $SUCCESS$ has $3$ $Ss$.

Consider the three Ss as one S (so that they are always together).

Then, the word $SUCCESS$ has $5$ letters of which there are $2$ $Cs$.

$\therefore \;$ Number of ways these 5 letters can be arranged amongst themselves $= \dfrac{5!}{2!} = \dfrac{5 \times 4 \times 3 \times 2!}{2!} = 60$ ways

$\therefore \;$ Number of ways the letters of the word $SUCCESS$ be arranged so that all $Ss$ are together $= 60$ ways.