$^{14}C_4 + \sum_{j=1}^{4} {^{18-j}C_3}$ is equal to

$A$ 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

There are two urns. Urn $A$ contains $3$ distinct red balls,and Urn $B$ contains $9$ blue balls. If two balls are selected at random from each urn and swapped,in how many ways can this operation be performed?

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

$\binom{15}{8} + \binom{15}{9} - \binom{15}{6} - \binom{15}{7} = \dots$

The value of ${ }^{16} C_{9}+{ }^{16} C_{10}-{ }^{16} C_{6}-{ }^{16} C_{7}$ is