The number of ways in which $15$ identical gold coins can be distributed among $3$ persons such that each one gets at least $3$ gold coins is

Compute $\frac{8!}{6! \times 2!}$

An engineer is required to visit a factory for exactly $4$ days during the first $15$ days of every month,and it is mandatory that no two visits take place on consecutive days. The number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is:

Out of $6$ books,in how many ways can a set of one or more books be chosen?

If ${}^nC_4, {}^nC_5$ and ${}^nC_6$ are in $A.P.$, then $n$ 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