In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then the range of $k$ is:

$A$ father with $8$ children takes $3$ children to the zoo at a time. If he can go more than once without taking the same $3$ children together,in how many ways can the father go to the zoo?

$A$ box contains $2$ white balls,$3$ black balls,and $4$ red balls. In how many ways can $3$ balls be drawn from the box if at least one black ball is to be included in the draw?

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

$A$ 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