$^{47}C_4 + \sum_{r=1}^5 {}^{52-r}C_3 = $

$A$ candidate is required to answer $6$ out of $12$ questions which are divided into two parts $A$ and $B$, each containing $6$ questions. The candidate is not permitted to attempt more than $4$ questions from any part. In how many different ways can he/she make his/her choice of $6$ questions?

The least value of a natural number $n$ such that $\binom{n-1}{5} + \binom{n-1}{6} < \binom{n}{7}$ is:

$A$ team of $11$ players is to be selected from $22$ players. If $2$ specific players must be included in every team and $4$ specific players must always be excluded,in how many ways can this selection be made?

In how many ways can two balls of the same color be selected from $4$ distinct black balls and $3$ distinct white balls?

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