The number of ways in which an examiner can assign $30$ marks to $8$ questions, giving not less than $2$ marks to any question, is

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is

An engineer is required to visit a factory for exactly four days during the first $15$ days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during 1$-15$ June $2021$ is. . . . . . 

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 $........$.

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards belong to four different suits,

If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to