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

In a group of $6$ boys and $4$ girls,four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

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:

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

In an examination hall,there are $4$ rows of chairs. Each row has $8$ chairs,$1$ behind the other. There are $2$ classes sitting for the examination with $16$ students in each class. It is desired that in each row,all students belong to the same class and that no $2$ adjacent rows are allotted to the same class. In how many ways can these $32$ students be seated?

The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. $A$ total number of $m$ points are taken on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$. The maximum number of triangles formed with vertices at these points is: