Combinatorics Questions

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 elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is:

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is:

Statement-1 : The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $\left(\genfrac{}{}{0ex}{}{9}{3}\right)$.Statement-2 : The number of ways of choosing any $3$ places from $9$ different places is $\left(\genfrac{}{}{0ex}{}{9}{3}\right)$.

Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is: