Let A 12345 and B 123456 How many one to one fuctions f A

Let A = {1,2,3,4,5} and B = {1,2,3,4,5,6}. How many one to one fuctions f: A --> B satisfy

a) f(1) = 3

b) f(1) = 3 and f(2) = 6

Solution

a)

In one to one function each element has a unique image ie no two elements can have the same image

Image of 1 is fixed as 3

2 can now be mapped to remaining 5 elements

3 to rest of 4 elements

4 to rest of 3 elements

5 to rest of 2 elements

So, 5*4*3*2=120 functions

b)

Now we are fixing two elements

SO, 3 can be mapped to remaining 4 elements

4 can be mapped to rest of 3 elements

5 to rest of 2 elements

So, 4*3*2=24 functions