The number of ways in which a team of $11$ players can be formed out of $25$ players,if $6$ out of them are always to be included and $5$ of them are always to be excluded,is

$A$ group consists of $8$ boys and $5$ girls. The number of committees of $5$ persons that can be formed,if the committee consists of at least $2$ girls and at most $2$ boys,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?

$A$ question paper is divided into two parts,$A$ and $B$,each consisting of $5$ questions. If a candidate has to select $6$ questions in total,in how many ways can they do so if they must select at least $2$ questions from each part?

If the number of subsets with $8$ elements from the set $A=\{a_1, a_2, a_3, \ldots, a_n\}$,$n \geq 8$,is five times the number of such subsets containing $a_4$,then $n=$

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is: