Question

How many number of binary operations can be done on a set with n elements?

Answer 1

A binary operation is performed on two elements to create a new element. Common binary operations are addition, subtraction, multiplication, and division.

Total number of binary operations that can be performed on n elements is $n^{n^2}$ which is n raised to the square of n  

Let’s assume if there are 4 elements then the number of binary operation possible with the 4 elements is $=4^{4^2}\\ \\=4^{16}$

Hence $4^{16}$ number of operations are possible with 4 elements.