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

The value of ${}^{50}C_4 + \sum_{r=1}^{6} {}^{56-r}C_3$ is

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-

There are $15$ persons in a party and each person shakes hands with every other person exactly once. The total number of handshakes is:

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?