If a team of $4$ persons is to be selected out of $4$ married couples to play a mixed doubles tennis game,then the number of ways of forming a team in which no married couple appears is:

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

If $\binom{a^2+a}{3} = \binom{a^2+a}{9}$,then $a = \dots$

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 $n=$

For a scholarship,at most $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selecting at least one candidate for the scholarship is $63$,then the maximum number of candidates that can be selected for the scholarship is -

The number of ways in which a cricket team of $11$ members can be formed out of $6$ batsmen,$6$ bowlers,$4$ all-rounders and $4$ wicket keepers by selecting at least $4$ batsmen,at least $3$ bowlers,at least $2$ all-rounders and only $1$ wicket keeper is: