The number of ways of distributing $3$ dozen fruits (no two fruits are identical) to $9$ persons such that each gets the same number of fruits is

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

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

Three letters,to each of which corresponds an envelope,are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes 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:

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