Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then the range of $k$ is:

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

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of exactly $3$ girls?

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these do the four cards belong to four different suits?

$A$ 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