How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?

If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^nC_{r-1} + ^nC_r = $

There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?

The number of numbers that can be formed with the help of the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy odd places,is

Each section in the first year of a plus $2$ course has exactly $40$ students. If there are $5$ sections,in how many ways can a set of $4$ student representatives be selected,$1$ from each section?

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?