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

is this where I use n!?

Answer 2

if they are distinct, then since there are 5 letters there are \(5!\) arrangements
that by the countining principle
5 choices for the first letter
4 for the second
3 for the third
2 for the fourth
1 for the last letter

Answer 3

if you cannot tell the two z's apart then you have to divide by the number of ways to arrange the two z's which is \(2!=2\) so
\[\frac{5!}{2}\]

Answer 4

so yes, this is where you use \(n!\)

Answer 5

so is it 120 for the first one and 60 for the second one?

Answer 6

@satellite73

Answer 7

am I correct?