If $^{n + 1}C_3 = 2 \cdot ^nC_2$,then $n =$

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

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

If $5$ dice are rolled simultaneously,then the number of ways of getting a total of $7$ on their faces is:

In an election,a voter can vote for any number of candidates but not more than the number of candidates to be elected. There are $10$ candidates and $4$ are to be elected. If a voter must vote for at least one candidate,in how many ways can they vote?

If $\binom{189}{35} + \binom{189}{x} = \binom{190}{x}$,then $x = \dots$