To find the number of arrangements possible using the letters in the word FUZZY with distinct Z's, we can treat each letter as distinct characters.
The word FUZZY has 5 letters, out of which Z is repeated twice. Therefore, the total number of arrangements possible is 5!/2! = 60.
If the letter Z is interchangeable with the other letters, then we can treat all Z's as indistinguishable. In this case, the word FUZZY has 4 distinguishable letters (F, U, Z, Y) out of which Z is repeated twice.
Therefore, the total number of arrangements possible is 4!/2! = 12 when Z is interchangeable with the other letters.
In conclusion, there are 60 arrangements possible when each Z is distinctly different, and 12 arrangements possible when Z is interchangeable with the other letters.
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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.
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