Out of $14$ cricket players,$5$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $4$ bowlers?

$A$ 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?

Determine $n$ if $^{2n}C_{3} : ^{n}C_{3} = 12 : 1$.

If $^{n + 1}C_3 = 2 \cdot ^nC_2$,then $n =$

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n$ equals

If a person has $3$ coins of different denominations,the number of different sums that can be formed is