$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to

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

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

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

If ${}^n{P_5} = 20 \cdot {}^n{P_3}$,then $n = $