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?

Answer 1

120, 60
First answer is 5!, second answer is 5!/2 because swapping two z's does not generate a new permutation.

Answer 2

Case 1: If the letter z is distinctly different

If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = 120 different arrangements

Case 2: If the letter Z is interchangeable

If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2

So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = 60 arrangements