How many distinct permutations can be made from the letters of the word "infinity"?

Question

The answer key that's in the book says it's 560. I tried 8! / 3! x 2! x 1! x 1! but that's equal to 3360. Can someone explain how to do this?

Answer 1

I I I N N F T Y

8 letters total = 8!

But divide by 3! (All I's are the same)

and 2! (ditto on the N's)

8 7 6 5 4 3 2 1

---------------------

2 1 3 2 1

8 7 6 5 2 = 56 * 60 = 3360 which is the right answer.

Maybe "560" was meant to be 56 x 60 ?

Or it's just a typo.  That happens sometimes

and the checkers don't catch it.

.

Answer 2

If all the letters are different, then the answer will be 8!

But there are 3"i"s and 2 "n"s.

Answer will therefore be 8!/(3!2!) = 3360.

The answer key in the book is wrong.