How many permutations can you make with the word infinite?

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How many permutations can you make with the word infinite?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I thought about counting each different letter and then doing by group.
what's the total number of letters ? and how many letters re repeating ?
8 letters, with N repeating twice and I repeating 3 times.

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Other answers:

(5 unique letters)
Got it. It would be the total divided by the total of each one.
alright nice \[\huge\rm \color{ReD}{i}\color{blue}{n}f\color{reD}{i}\color{blue} {n}\color{ReD}{i}te \] \[\huge\rm \frac{ 8! }{ \color{Red}{3!}\color{blue}{2!} }\]
yes right total number divide by total number of repeating letters
Thanks a lot. My problem is to distinguish which of so many formulas to use hehe
now solve to find final answer**
3360 :)
hahah well you don't need formula for this one
I know, I just get confused sometimes
3360 ?
Yep
doesn't looks right.
Actually it is the correct answer in the book :)
ohh nvm *facepalm* i solved `6!` over 3!2!
Hehe thanks for all the help :)
yes 3360

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