In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

If $\alpha = ^mC_2$,then $^\alpha C_2$ is equal to

The number of positive integers less than $10000$ which contain the digit $5$ at least once is

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

The number of $9$-digit even natural numbers formed using only the digits $0$ and $1$,such that no two consecutive digits are $0$,is: