How many one-to-one correspondences are there between two sets with 4 elements each?
A)None
B)2
C)24
D)6

Question

Quizplus · Accepted Answer

A one-to-one correspondence (bijection) between two sets of equal size means each element in one set is paired with exactly one unique element in the other set, and vice versa. For the first element in the first set, there are 4 choices in the second set. For the second element, there are 3 remaining choices, then 2 for the third, and finally 1 for the last. This gives us 4! (4 factorial) possibilities, which is 4*3*2*1 = 24.

How Many One-To-One Correspondences Are There Between Two Sets with 4