From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there on the committee. In how many ways can it be done?

In how many ways can five examination papers be arranged so that physics and chemistry papers never come together?

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that each team includes exactly $3$ bowlers and $1$ wicket-keeper?

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

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,is

The solution set of $^{10}C_{x-1} > 2 \cdot ^{10}C_x$ is