Probability/statistics problem!

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 interchangeable with the other? Explain your reasoning.

Can someone please guide me through the steps to solving this?

Question

Probability/statistics problem!

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 interchangeable with the other? Explain your reasoning. 

Can someone please guide me through the steps to solving this?

anonymous · Answer

@Mertsj

mertsj · Answer

The number of arrangements of Fuzzy is 5! if the z's are considered different.

mertsj · Answer

If they are interchangeable, you must divide 5! the the 2! arrangements of the 2 z's

anonymous · Answer

Is there any work I can show for that? how do you figure that out?

anonymous · Answer

how do you figure out the 5! first of all?

mertsj · Answer

Number of Permutations of 5 items.  How do you show that?

anonymous · Answer

Oh ok lol, I guess all I really need is to explain my reasoning at the end.