SOLUTION: how many one-to-one correspondences are there between two sets with k elements each?

Question 1196436: how many one-to-one correspondences are there between two sets with k elements each?
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
.


ANSWER.  k! = 1*2*3* . . . *(k-1)*k.



Explanation.


Let the sets be A and B: they have equal numbers of elements.


1st element of A can be related to any of k elements of B.

2nd element of A can be related to any of remaining (k-1) elements of B.

3rd element of A can be related to any of remaining (k-2) elements of B.


   . . . and so on . . . 


It gives the answer.

Solved and explained.

--------------

The problem is the same as to ask

        " how many are there permutations of a set of k elements ? "

RELATED QUESTIONS
How many one to one correspondences are there between two sets with 5 elements... (answered by stanbon)

How many one-to-one correspondences are there between the two sets {1,2,3,4...12} and... (answered by stanbon)

How many one to one correspondences are there between the sets {x,y,z,u,v} and... (answered by stanbon)

Can you please explain this to me? Thanks so much in advance for your time! If D = {w, (answered by stanbon)

5. If D = {w, h, y} and E = {n, o, t}then answer the following: (a) How many possible... (answered by Edwin McCravy)

5. If D = {w, h, y} and E = {n, o, t}then answer the following: (a) How many possible... (answered by stanbon,solver91311)

How many different one-to-one correspondences could be listed between the vertices of two (answered by stanbon)

How many different one-to-one correspondences could be listed between the vertices of two (answered by Maria c)

Please can you help me solve this work problem question. How many one to one functions... (answered by ikleyn)