The number of different signals which can be given from $7$ different coloured sheets,taking one or more at a time is

The number of natural numbers less than $10000$ which are divisible by $5$ and in which no digit is repeated is:

If all possible $4$-digit numbers are formed by choosing $4$ different digits from the given digits $1, 2, 3, 5, 8$,then the sum of all such $4$-digit numbers is:

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

The total number of $7$-digit numbers that can be formed using only the digits $1, 2,$ and $3$ such that the sum of the digits is $10$ is:

In a group of $3$ girls and $4$ boys,there are two boys $B_1$ and $B_2$. The number of ways in which these girls and boys can stand in a queue such that all the girls stand together,all the boys stand together,but $B_1$ and $B_2$ are not adjacent to each other,is: