Question

iii. State the relation between the order of a group and the number of binary operations that can be defined on that set. How many binary operations can be defined on a set with 4 elements?

Answer 1

Recall that the order of a group is the number of elements in the group

number of binary  operations equals to n^n*n. So for a set with 4 elements we have 4¹⁶=4294967296 operations