If $C(n, 8) = C(n, 6)$,find $C(n, 2)$.

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is