No. of arrangements of letters of SUCCESS such that first C precedes first S 
In how many ways can we arrange the letters of the word SUCCESS such that the first C precedes the first S

My attempt
there are four strings that satisfy the above condition, namely $$CSSSC, CSSCS, CSCSS, CCSSS$$
Now, we need to arrange $U, E$. In each string, there are six gaps where we can place our $U,E$. Since, each gap can contain both $U$ and $E$ , either one of them or neither. Thus, number of ways of arranging $U$ and $E$ is 36. Thus, number of arrangements should be $36 \cdot 4=144$. Answer is given $168$. Can anyone point out where am I going wrong

Consider one of the $4$ arrangements of letters $C$ and $S$, like your first one $.C.S.S.S.C.$, the issue is to place $E$ and/or $U$ in one of the $6$ slots (materialized by the dots), which amounts to count the number of functions from the set of $2$ elements $\{E,U\}$ to the set of slots $S$ with six elements, which makes $6^2=36$ such functions (your count), but there are $6$ particular functions that must be counted twice, those sending $E$ and $U$ onto the same slot. In this case, and only in this one, we have to specify an order: $EU$ or $UE$.
Therefore the total count is:
$$4 \times (36+6)=168.$$
