The sum of all the $4$-digit numbers formed by taking all the digits from ${2, 3, 5, 7}$ without repetition is:

The number of even numbers greater than $1000000$ that can be formed using all the digits $1, 2, 0, 2, 4, 2, 4$ is

There are $3$ applicants for a scholarship in Physics,$5$ for Mathematics,and $4$ for Chemistry. In how many different ways can one of these scholarships be awarded?

$A$ box contains $5$ blue, $6$ yellow, and $4$ red balls. The number of ways of drawing $8$ balls containing at least two balls of each color is:

In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?

The number of four-digit natural numbers which contain exactly two distinct digits is: