There are $4$ letters and $4$ envelopes. If the letters are placed into the envelopes at random,find the probability that all letters are placed in the wrong envelopes.

There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope is:

There are $7$ greeting cards, each of a different colour, and $7$ envelopes of the same $7$ colours as the cards. The number of ways in which the cards can be put in envelopes, so that exactly $4$ of the cards go into envelopes of the respective colour, is:

$A$ person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:

Let the set $S = \{2, 4, 8, 16, \ldots, 512\}$ be partitioned into $3$ sets $A, B, C$ with an equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$. The number of such possible partitions of $S$ is equal to:

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