In how many ways can $10$ people be seated in $2$ boats such that each boat has $5$ people and two specific people do not sit in the same boat?

If $^nC_{r-2} = 36$,$^nC_{r-1} = 84$,and $^nC_r = 126$,then the value of $^nC_{2r}$ is

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

There are ten boys $B_{1}, B_{2}, \ldots, B_{10}$ and five girls $G_{1}, G_{2}, \ldots, G_{5}$ in a class. The number of ways of forming a group consisting of three boys and three girls,such that $B_{1}$ and $B_{2}$ are not both members of the same group,is

$A$ lady gives a dinner party for $6$ guests. The number of ways in which they may be selected from among $10$ friends,if two of the friends will not attend the party together,is:

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is: