The letters of the word $ASSASSIN$ are written down at random in a row. The probability that no two $S$ occur together is

Consider the following statements:
$(i)$ The number of one-one functions from set $A$ to set $B$,where $O(A) = m$ and $O(B) = n$ $(m \leq n)$,is given by ${}^n P_m$.
(ii) The number of ways in which $n$ people can be arranged at a circular table is $\frac{(n-1)!}{2}$.
(iii) The number of ways of selecting at least one thing out of the given $n$ distinct things is $2^n - 1$.
(iv) The number of ways in which $n$ distinguishable objects can be distributed into $k$ distinguishable bins is ${}^n C_{k-1}$.
Which of the following is true?

The number of different words that can be formed from the letters of the word $SUCCESS$ in which the two $C$ are together but no two $S$ are together are:

If $a_n = \sum_{r=0}^n \frac{1}{^nC_r}$,then $\sum_{r=0}^n \frac{r}{^nC_r}$ equals

The value of $\sum\limits_{r = 1}^{15} {{r^2} \left( \frac{^{15}C_r}{^{15}C_{r - 1}} \right)}$ is equal to

The word $UNIVERSITY$ is arranged randomly. The probability that both $I$s do not come together is: