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

Algebra ->  sets and operations -> SOLUTION: how many one-to-one correspondences are there between two sets with k elements each?      Log On


   

Question 1196436: how many one-to-one correspondences are there between two sets with k elements each?
Answer by ikleyn(52790) About Me  (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 ? "