How many different word can be formed by the word MISSISSIPPI 

The word "MISSISSIPPI" consists of 11 letters, with repeated letters: 

- M appears 1 time
- I appears 4 times
- S appears 4 times
- P appears 2 times

The formula for calculating the number of distinct permutations of a multiset (where some elements repeat) is:

\[
\frac{n!}{n_1! \times n_2! \times \cdots \times n_k!}
\]

Where:
- \( n \) is the total number of letters,
- \( n_1, n_2, \dots, n_k \) are the factorials of the repeated elements.

For "MISSISSIPPI," the formula becomes:

\[
\frac{11!}{1! \times 4! \times 4! \times 2!}
\]

Now let's calculate this:

\[
11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 39,916,800
\]

\[
4! = 4 \times 3 \times 2 \times 1 = 24
\]
\[
2! = 2 \times 1 = 2
\]

So the number of distinct words that can be formed is:

\[
\frac{39,916,800}{1 \times 24 \times 24 \times 2} = \frac{39,916,800}{1,152} = 34,650
\]

Thus, 34,650 different words can be formed using the letters of "MISSISSIPPI."

Would you like a detailed explanation of the steps? 

Here are 5 related questions:
1. How would the result change if another "M" was added?
2. What is the formula for finding permutations of a multiset?
3. How do you calculate factorials?
4. What if there were no repeated letters in the word?
5. How would adding an "A" to the word affect the permutations?

**Tip:** Understanding how to handle repeated elements in permutations is key for solving similar problems efficiently.

How many different words can be formed by the word MISSISSIPPI

Learn how to calculate the number of different words that can be formed from the word MISSISSIPPI, accounting for repeated letters. This problem uses the permutation formula for multisets and explores concepts like factorials and combinatorics. Suitable for students in Grades 10-12.

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