Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all,then the number of ways in which the selection can be made is:

In an apartment,there are $30$ kids. If each kid plays table tennis with every other kid exactly once,then the total number of matches played by them is:

In how many ways can $10$ balls be divided between two boys,such that one receives $2$ balls and the other receives $8$ balls?

The total number of all those $3$-digit numbers in which the sum of all the digits in each of them is $10$,is

In how many ways can $4$ balls be picked from $6$ black and $4$ green colored balls such that at least one black ball is selected?