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.

I know that since there are five letters, there are 5 places so the possibilities for the 1st spot is 5, 2nd is 4, 3rd is 3, 4th is 2, and 5th is 1, so it's 5*4*3*2*1, which equals 120 so there are 120 possible arrangements, but I don't quite understand the second question.

Question

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.

I know that since there are five letters, there are 5 places so the possibilities for the 1st spot is 5, 2nd is 4, 3rd is 3, 4th is 2, and 5th is 1, so it's 5*4*3*2*1, which equals 120 so there are 120 possible arrangements, but I don't quite understand the second question.

anonymous · Answer

so a. is 5*4*3*2*1/2*1= 120/2 and b. is 5*4*3*2*1=120?

anonymous · Answer

@Luis_Rivera

anonymous · Answer

and by a and b you mean the 1st question and second question right?

anonymous · Answer

thanks so much:)

anonymous · Answer

I think the answers should be opposite though ...I mean first should be 5! and second 5!/2!... can you help???

anonymous · Answer

I guess that is right

anonymous · Answer

which one??? the former  or the latter???

anonymous · Answer

I think the 1st is 5! and the second is 5!/2!

anonymous · Answer

That means mine... the one I proposed???

anonymous · Answer

ya

anonymous · Answer

Because the first case says they must be distinctly different from each other... that means both z's are different... we can think them of as replace one of them by another symbol... i.e. 5 different symbols are there... 
Hope this makes sense :-)