In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

$^nC_{r+1} + ^nC_{r-1} + 2^nC_r = \dots$

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are two red cards and two black cards?

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

The number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

$^{n-1}C_3 + ^{n-1}C_4 > ^nC_3$,then the value of $n$ is