Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

There are $m$ points on a straight line $AB$ and $n$ points on another line $AC$,none of them being the point $A$. Triangles are formed from these points as vertices when $(i)$ $A$ is excluded and $(ii)$ $A$ is included. Then the ratio of the number of triangles in the two cases is

The number of words that do not start and end with vowels,formed using all the letters of the word $UNIVERSITY$ such that all vowels are in alphabetical order,is

The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

The sum of the digits in the unit's place of all the $4-$digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is

$3$ boys $B_1, B_2, B_3$ and $6$ girls $G_1, G_2, . . . , G_6$ are to be seated in a row. The number of ways they can be seated such that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to: