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
Best Answer
Take for example, $CSSSC$. Place a $U$ in one of the six gaps like this $CSSUSC$. Now you have six letters and seven available gaps to place an $E$. Hence $4\times 6 \times 7=168$.