Find the number of distinct arrangements of the 8 letters in SLIPPERS.Two of the same letter are considered identical (not distinct).
Question
Find the number of distinct arrangements of the 8 letters in SLIPPERS.
Two of the same letter are considered identical (not distinct).
Solution
To solve this problem, we use the formula for permutations of multiset: n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of item.
In the word "SLIPPERS", there are 8 letters in total.
- There are 2 S's.
- There are 2 P's.
- There is 1 L.
- There is 1 I.
- There are 2 E's.
- There is 1 R.
So, we plug these values into the formula:
8! / (2! * 2! * 1! * 1! * 2! * 1!) = 40,320 / (2 * 2 * 1 * 1 * 2 * 1) = 40,320 / 8 = 5,040.
So, there are 5,040 distinct arrangements of the letters in "SLIPPERS".
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