In a conference of $8$ persons, if each person shake hand with the other one only, then the total number of shake hands shall be

In a touring cricket team there are $16$ players in all including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players from these, can be chosen, so as to include three bowlers and one wicket-keeper

Let $A=\left[a_{i j}\right], a_{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$. The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is $........$.

If $^n{C_r} = 84,{\;^n}{C_{r - 1}} = 36$ and $^n{C_{r + 1}} = 126$, then $n$ equals

In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is

The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included