Question

How many ways are there of rearranging the letters MATH such that each letter is replaced by a different one?

Answer 1

?

Answer 2

lol, that doesn't answer the question.

Answer 3

I know that all the arrangements of math are 4!

Answer 4

yeah

Answer 5

but I need to find how many possibilities remain once I rearrange them.

Answer 6

what do you mean?

Answer 7

Like no letters can be in the same place. So it starts our as MATH. it could be THAM or AMHT.

Answer 8

But it could not be MAHT because M and A are still in their initial positions

Answer 9

3!

Answer 10

?

Answer 11

how many choices for the first spot?

Answer 12

right, there would be 3! spots for the first slot

Answer 13

So we start with 4! and then we need to subtract away some possibilities

Answer 14

what does that do?

Answer 15

It would be like this for all of the letters