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

The number of ways of dividing $200$ dissimilar things into $10$ groups each containing $20$ elements is

In an examination,$5$ students have been allotted their seats as per their roll numbers. The number of ways,in which none of the students sits on the allotted seat,is $..........$.

The set $S = \{1, 2, 3, \dots, 12\}$ is to be partitioned into three sets $A, B, C$ of equal size such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \emptyset$. The number of ways to partition $S$ is:

$150$ students took admission. In how many ways can they be divided into three equal sections $A, B,$ and $C$?

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