Find the number of permutations of the letters of the word MISSISSIPPI.
Question
Find the number of permutations of the letters of the word MISSISSIPPI.
Solution
To find the number of permutations of the letters in the word MISSISSIPPI, we can use the formula for permutations of a word with repeated letters.
Step 1: Count the number of times each letter appears in the word. In this case, we have:
- M appears once
- I appears four times
- S appears four times
- P appears two times
Step 2: Calculate the factorial of the total number of letters in the word. In this case, we have 11 letters, so the factorial is 11!.
Step 3: Divide the factorial by the product of the factorials of the number of times each letter appears. In this case, we have:
- 11! / (1! * 4! * 4! * 2!)
Step 4: Simplify the expression. In this case, we have:
- 11! / (1! * 4! * 4! * 2!) = 34,650
Therefore, there are 34,650 permutations of the letters in the word MISSISSIPPI.
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