Which would be correct: $$P_4=4!=24 \quad \text{or} \quad \frac{4!}{1!2!1!}=12?$$
I don't know if Meеt and Meеt with exchanging the two $e$'s are different or not?
If the answer is the latter, why would it be different from the permutations of the word Meat with an $a$, which should be $24$ permutations I believe?
Thanks.
Best Answer
This is not a matter of mathematics. You already gave the correct answer to your own question: It depends if you treat the two $e$'s as identical (then you have $12$ permutations) or as distinguishable (in this case you have $24$ permutations). Mathematics can't help you to decide which one fits for you.
If the word is written on a computer, using any standard text editor, then both $e$'s are identical, even if you look deep into the electronic storage. This gives you $12$ permutations.
But if you hand out colored pens to a child, ask him or her to write the word on a piece of paper, and then cut out the four letters and shift them around on your table, you will easily be able to distinguish the two versions of the letter $e$. So now you will find $24$ permutations.