How to calculate the no of the following from a set (1,2,3,......n) to itself?

1.one-one function

2.onto function

3.binary operation

1. The number of one-one functions possible are n!.

 

For first element has n choices and second has n-1 and so on.

 

2. The number of onto functions possible are n^n.

 

every element in the co-domain has n choices.

 

3. The number of binary operations possible are (n)^n²