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

How many numbers greater than $24,000$ can be formed by using the digits $1, 2, 3, 4, 5$,when no digit is repeated?

If $^{20}C_{n+2} = ^nC_{16}$,then the value of $n$ 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

If $a_n = \sum_{r = 0}^n \frac{1}{^nC_r}$,then $\sum_{r = 0}^n \frac{r}{^nC_r}$ equals

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?