Enumeration of Relations and Functions between two finite sets has always been an interesting study in Combinatorics, a branch of mathematics which is seen as art of counting without actual counting. In this paper, we discuss the enumeration of various relations and functions. Interestingly enough, the answers turns out be part of interesting class of numbers.

Keywords: Equivalence Relations, One-One Functions, Onto Functions, Stirling’s Numbers of Second Kind, Bell Numbers, Multinomial coefficients