How many arrangements are possible using the letters in the word FUZZY if each letter "Z" is distinctly different than the other? How many arrangements are possible if the letter "Z" is interchangeabe with the other? Explain your reasoning.

Answer 1

You use a factorial (!) with the number of articles given. A factorial is a product of an integer and all integers below it.

5 Factorial
5! = ___ combinations

Answer 2

(a)
"Z" is distinctly different than the other: I think that means you have to count both of them, as if they're different letters.
There are five letters in total. Therefore,
5! = 120 ways

(b)
"Z" is repeated twice in the word FUZZY. Thus,
5! / 2! = 60 ways

hope this helps~ `u`