Find the number of seven letter words that can be formed by using the letters of the word SUCCESS so that the two C are together but no two S are together.

Explanation

We have letters (S,S,S),U,(C,C),E.
Let us first arrange (C,E),U and E.
Considering C C as single object, U, C,C,E can be arranged in 3! Ways.
`xxUxx(C C)xxExx`.
Here four gaps are created, marked with `xx`.
Since no tow S are together, three S's can be put in places marked with `xx`.
Three places can be selected in `.^(4)C_(3)` ways, in which S's can be arranged in one way.
So, total number of arrangements `=3!xx .^(4)C_(3)=24`.