Let A abcd and S 123456 Find the number of onetoone functi

Let A = {a,b,c,d} and S = {1,2,3,4,5,6}

Find the number of one-to-one functions g : A -> S

Solution

Note that in a function an element can map to only one element

So, here g maps one element of A to only one element of S

If g is one to one we have the condition no two elements in A get mapped to same element in S

Hence since A has 4 elements , image set of g will also have 4 elements.

So we can find all one to one functions this way

Map a to any of the 6 elements in S

Then, map b to any of the other 5 elements in S

Then , map c to any of the other 4 elements in S

Then, map d to any of the other 3 elements in S

So, total functions are:

6*5*4*3=360 functions.