In how many ways can a garland be made from exactly $10$ flowers?

$P, Q, R$ and $S$ have to give lectures to an audience. The organiser can arrange the order of their presentation in ............. ways.

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals

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

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is:

In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?