There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
$36$
$108$
$99$
$165$
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{ n +1} C _{2}+2\left({ }^{2} C _{2}+{ }^{3} C _{2}+{ }^{4} C _{2}+\ldots+{ }^{ n } C _{2}\right)$ is ...... .
The number of triplets $(x, y, z)$. where $x, y, z$ are distinct non negative integers satisfying $x+y+z=15$, is
The number of ordered pairs ( $\mathrm{r}, \mathrm{k}$ ) for which $6 \cdot ^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)\cdot{^{36} \mathrm{C}_{\mathrm{r}+1}}$. where $\mathrm{k}$ is an integer, is
How many words, with or without meaning, can be formed using all the letters of the word $\mathrm{EQUATION}$ at a time so that the vowels and consonants occur together?