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

If the letter z's are distinctly different, there are P(5,5) arrangements. That is

`P\left(5,5\right)=5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120`

If the z's are interchangeable, the number of different arrangements is given by

`(5!)/(2!)=5\cdot 4\cdot 3=60`