The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

The least value of natural number $n$ satisfying $C(n, 5) + C(n, 6) > C(n + 1, 5)$ is

There are $7$ men and $8$ women in a club. $A$ committee is formed using these persons. What will be the number of ways to select $6$ persons such that at least one is a woman?

There are $6$ members to be selected for a group to be sent abroad from a total of $12$ members. In how many ways can the selection be made such that a particular member is always excluded?

The number of functions $f$ from $\{1, 2, 3, \dots, 20\}$ to $\{1, 2, 3, \dots, 20\}$ such that $f(k)$ is a multiple of $3$ whenever $k$ is a multiple of $4$ is:

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first $2$ questions have $3$ choices each,the next $2$ have $4$ choices each,and the last $2$ have $5$ choices each?