Choose the correct number of ways in which $15$ different books can be divided into $5$ heaps of equal number of books.

Five letters are placed at random in five addressed envelopes. The probability that all the letters are not dispatched in the respective right envelopes is

There are $4$ balls of different colors and $4$ boxes of the same colors as the balls. In how many ways can $2$ balls be placed in the boxes such that they do not match their respective colors?

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

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

The set $S = \{1, 2, 3, \dots, 12\}$ is partitioned into three sets $A, B, C$ of equal size such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \phi$. In how many ways can $S$ be partitioned?