In how many ways can $52$ cards be distributed equally among four players?

Among the $5$ married couples, if the names of $5$ men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his wife is

$A$ person writes letters to $6$ friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?
Notation : $D_n = n! \left( \sum_{i=0}^n \frac{(-1)^i}{i!} \right)$

If there are $6$ letters and $6$ corresponding envelopes,in how many ways can all the letters be placed in the wrong envelopes?

Let $A = \{x_1, x_2, x_3, x_4\}$ and $B = \{y_1, y_2, y_3, y_4\}$. $A$ function $f: A \to B$ is defined. The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

If $4$ letters are placed randomly into $4$ envelopes,what is the probability that none of the letters are placed in their correct envelopes?