How many ways can you arrange the letters in the word "three"
Question
How many ways can you arrange the letters in the word "three"
Solution
The word "THREE" has 5 letters in total. However, the letter "E" is repeated twice.
The formula for permutations of a multiset (a set in which members can repeat) is:
n! / (r1! * r2! * ... * rk!)
where:
- n is the total number of items,
- r1 through rk are the numbers of each type of item.
In this case, n = 5 (the total number of letters), r1 = 2 (the number of "E"s), and all other r's are 1 (since all other letters only appear once).
So, the number of ways to arrange the letters in "THREE" is:
5! / (2! * 1! * 1! * 1! * 1!) = 120 / 2 = 60 ways.
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