How many ways can be the
letters of COMMITTEE be arranged?

The word **COMMITTEE** consists of 9 letters in total. However, some of these letters repeat, so we need to account for those repetitions when calculating the number of distinct ways to arrange the letters.

The breakdown of the letters is:
- C: 1 occurrence
- O: 1 occurrence
- M: 1 occurrence
- I: 1 occurrence
- T: 2 occurrences
- E: 2 occurrences

To calculate the number of distinct arrangements of the letters in the word COMMITTEE, we use the formula for permutations of multiset:

\[
\text{Number of arrangements} = \frac{n!}{k_1! \cdot k_2! \cdot \cdots \cdot k_r!}
\]

where:
- \( n \) is the total number of letters (9 in this case),
- \( k_1, k_2, \dots, k_r \) are the factorials of the frequencies of the repeated letters.

Thus, the formula becomes:

\[
\frac{9!}{2! \cdot 2!}
\]

Now, let's calculate it:

\[
9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362880
\]
\[
2! = 2 \times 1 = 2
\]
\[
\frac{362880}{2! \cdot 2!} = \frac{362880}{2 \times 2} = \frac{362880}{4} = 90720
\]

So, the number of distinct ways the letters of COMMITTEE can be arranged is **90,720**.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. How many distinct ways can the letters of the word "SCHOOL" be arranged?
2. What if no letter is repeated in the word COMMITTEE, how would you calculate its permutations?
3. How would the result change if we added another "T" to the word COMMITTEE?
4. How do you calculate the permutations if all letters are unique?
5. What is the formula for arranging items with restrictions on their position?

**Tip:** When calculating permutations with repeated elements, remember to divide by the factorial of each frequency of repeated letters!

How many ways can the letters of COMMITTEE be arranged?

Discover how to calculate the number of distinct ways to arrange the letters in the word COMMITTEE. This problem involves calculating permutations with repeated elements and uses the formula for multisets. The solution includes step-by-step calculations and is suitable for students in Grades 9-12.

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