The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

All possible $5$-digit numbers,each having $5$ distinct digits,are formed using the digits $\{1, 2, 3, 5, 6, 8\}$. Among them,the number of such numbers which are divisible by $3$ but not by $6$ is:

$A$ $5$-digit number $\overline{abcde}$,when multiplied by $9$,gives the $5$-digit number $\overline{edcba}$. The sum of the digits in the number is:

If $\sum\limits_{r = 0}^{25} {\left( {^{50}C_r \cdot ^{50 - r}C_{25 - r}} \right) = K\left( {^{50}C_{25}} \right)}$,then $K$ is equal to

If $P(n, r) = 1680$ and $C(n, r) = 70$,then $69n + r! = \dots$.

In how many ways can $3n$ distinct objects be distributed equally among $3$ persons?