If set $A$ contains $8$ elements,then the number of subsets of $A$ which contain at least $6$ elements is

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

The number of four-digit numbers that can be formed using all the digits from $1$ to $9$ (excluding zero) such that every number has exactly $2$ distinct digits is:

If a committee consists of $3$ men and $2$ women,in how many ways can a committee of $5$ members be formed from $5$ men and $4$ women?

There are $10$ persons named $A, B, \dots, J$. We have space to keep only $5$ of them. If $A$ must be included,and $G$ and $H$ must not be included in the group of $5$,in how many ways can we arrange the group in a row?

If $5$ dice are rolled simultaneously,then the number of ways of getting a total of $7$ on their faces is: