In how many ways can a pack of $52$ cards be divided into four equal groups?

If $5$ letters are to be placed in $5$ addressed envelopes,then the probability that at least one letter is placed in the wrongly addressed envelope 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:

There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope is:

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

$n$ distinct items $1, 2, 3, \dots, n$ are arranged in $n$ distinct positions $1, 2, 3, \dots, n$. What is the probability that at least three items are in their correct positions?