In how many ways can $6$ letters be posted in $5$ letter boxes available in the locality?

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

The number of values of $r$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2} = ^{69}C_{r^2-1} - ^{69}C_{3r}$ is:

If ${}^n{P_5} = 20 \cdot {}^n{P_3}$,then $n = $

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval