Question

. If D = {w, h, y} and E = {n, o, t} then answer the following:
(a) How many possible one-to-one correspondences are there between sets D and E?
Will someone please explain why it is 6?

Answer 1

anyone?

Answer 2

it is 6 for sure and that is because
\[6=3\times 2\times 1\]

Answer 3

you want a one to one correspondence. pick a letter from set D
you have 3 choices of letters in set E to send it to.
then pick another letter from set D
now you have only two choices of letter in E to send it to because one is already taken
then the last letter in D has no choices, because you have used up two of the three letters from E

there are 3 ways to do the first task, 2 for the second, and 1 for the third. by the "counting principle" there are
\[3\times 2\times 1=6\] ways to do them together

Answer 4

in any case 6 is a small enough number that you could list all 6 possibilities