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 just need help setting the problem up, and I should be able to do the rest. Thank you!

Answer 1

How many arrangements are possible using the letters in the word FUZZY if each letter "Z" is distinctly different than the other?


We have 5 slots for each of the letters

Slot1 = 5 choices
slot2 = 4 choices (since you can't reuse a letter chosen beforehand)
slot3 = 3 choices
slot4 = 2 choices
slot5 = 1 choice

multiply out the choices to get ???

Answer 2

120?

Answer 3

correct

Answer 4

so that's for the first part

Answer 5

Okay...isn't that the same as saying "5!"?

Answer 6

Okay....that seemed easy lol

Answer 7

it is

Answer 8

5! = 120

Answer 9

How many arrangements are possible if the letter "Z" is interchangeable with the other?

Answer 10

We have 2 copies of Z. So the answer to this second part isn't 120 because we overcount if the Zs are indistinguishable.

Since we're double counting we have to divide 120 by 2 to get 120/2 = 60

Answer 11

That's it? wow I cannot think today :(