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

Question

anonymous · Answer

?

anonymous · Answer

lol, that doesn't answer the question.

anonymous · Answer

I know that all the arrangements of math are 4!

anonymous · Answer

yeah

anonymous · Answer

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

anonymous · Answer

what do you mean?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

3!

anonymous · Answer

?

anonymous · Answer

how many choices for the first spot?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

what does that do?

anonymous · Answer

It would be like this for all of the letters 

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