How many groups can be selected for playing football out of $5$ ladies and $4$ gentlemen such that there should be one lady and one gentleman on each side?

If the four-letter words (need not be meaningful) are to be formed using the letters from the word "$MEDITERRANEAN$" such that the first letter is $R$ and the fourth letter is $E,$ then the total number of all such words is

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is:

There are $6$ candidates for $3$ posts. In how many ways can the posts be filled?

Let $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is:

The sum of the digits in the unit place of all numbers formed with the help of $3, 4, 5, 6$ taken all at a time is