$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels?

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:

$A$ student is allowed to select at most $n$ books from a collection of $(2n+1)$ books. If the total number of ways in which one can select at least one book is $255$,then the value of $n$ is

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.

$A$ question paper has two sections $A$ and $B$,in which section-$A$ has $8$ questions and section-$B$ has $6$ questions. $A$ student has to answer a total of $10$ questions,choosing at least $4$ questions from section-$A$ and at least $3$ questions from section-$B$. The number of ways a student can answer the paper is: