Compute $\frac{12!}{10! \times 2!}$

The domain of the function $f(x) = {}^{(10-x)}C_{(x-6)}$ is...

$A$ team of $5$ students is to be selected from $12$ students. If two particular students are to be included in that team,then the number of ways that such team can be selected is

If ${ }^{15} C_4+{ }^{15} C_5+{ }^{16} C_6+{ }^{17} C_7+{ }^{18} C_8={ }^{19} C_{r}$,then the value of $r$ is equal to

Number of ways of arranging $8$ identical books into $4$ identical shelves where any number of shelves may remain empty is equal to

$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls?