There are $3$ candidates for a post and one is to be selected by the votes of $7$ men. The number of ways in which votes can be given is

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball,is

The sum of the divisors of $2^5 \cdot 3^4 \cdot 5^2$ is

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

When all the students in a school are made to stand in rows of $54,$ $30$ such rows are formed. If the students are made to stand in rows of $45,$ how many such rows will be formed?

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