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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).

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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.

  1. There are 2 S's.
  2. There are 2 P's.
  3. There is 1 L.
  4. There is 1 I.
  5. There are 2 E's.
  6. 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".

This problem has been solved

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