In how many ways can $3n$ distinct objects be distributed equally among $3$ persons?

If $x={ }^{16} C_5+{ }^{12} C_4, y=\sum_{r=1}^3{ }^{(20-r)} C_4, z=\sum_{k=1}^4{ }^{(16-k)} C_3$,then $x+y+z=$

If $^n{P_r} = 840$ and $^n{C_r} = 35$,then $n$ is equal to

For integers $n$ and $r$,let $\binom{n}{r} = \begin{cases} ^{n}C_{r}, & \text{if } n \geq r \geq 0 \\ 0, & \text{otherwise} \end{cases}$. The maximum value of $k$ for which the sum $\sum_{i=0}^{k}\binom{10}{i}\binom{15}{k-i} + \sum_{i=0}^{k+1}\binom{12}{i}\binom{13}{k+1-i}$ exists,is equal to ...... .

The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word $INCONVENIENCE$ is:

Three letters are chosen at random from the letters of the word $VARIABLE$ and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is