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?

How many words can be made from the letters of the word $BHARAT$ in which $B$ and $H$ never come together?

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval

$^{80}C_{40}$ is not divisible by -

In how many ways can a committee consisting of $5$ men and $6$ women be formed from $8$ men and $10$ women?

There are $4$ parcels and $5$ post-offices. In how many different ways can the registration of the parcels be made?