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The problem asks to find how many distinct word arrangements can be made from the letters of two given words:

1. **SANTAI**
2. **MISSISSIPI**

Let's solve these one by one:

### A. SANTAI
The word "SANTAI" contains the letters: S, A, N, T, A, I. We have:

- 6 letters in total.
- A appears twice, while all other letters (S, N, T, I) appear only once.

The formula to calculate the number of distinct arrangements when there are repeated letters is:
\[
\frac{n!}{k_1! k_2! \dots k_r!}
\]
Where:
- \( n \) is the total number of letters.
- \( k_1, k_2, \dots, k_r \) are the factorials of the frequencies of each repeated letter.

For **SANTAI**:
\[
n = 6, \quad \text{and A appears twice, so} \quad k_1 = 2
\]
The number of distinct arrangements is:
\[
\frac{6!}{2!} = \frac{720}{2} = 360
\]

### B. MISSISSIPI
The word "MISSISSIPI" contains the letters: M, I, S, S, I, S, S, I, P, I. We have:

- 11 letters in total.
- I appears 4 times.
- S appears 4 times.
- M and P each appear once.

Using the same formula:
\[
n = 11, \quad k_1 = 4 \ (\text{for I}), \quad k_2 = 4 \ (\text{for S})
\]
The number of distinct arrangements is:
\[
\frac{11!}{4!4!} = \frac{39916800}{24 \times 24} = \frac{39916800}{576} = 69300
\]

### Final Answers:
- A: The number of distinct arrangements for "SANTAI" is **360**.
- B: The number of distinct arrangements for "MISSISSIPI" is **69300**.

Would you like further details or clarifications on this process?

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**Related Questions:**
1. How would the result change if there were no repeated letters in the word?
2. What is the general approach to finding permutations of words with repeated letters?
3. How do you calculate the factorial of large numbers efficiently?
4. What happens if a word contains more than two repeated letters?
5. Can the same method be used for non-alphabetic characters, like numbers or symbols?

**Tip:** For problems involving word arrangements, always first check how many letters repeat and use the formula for permutations with repetition!

Tentukan banyak susunan kata berbeda yang dapat dibentuk dari huruf pembentuk kata: A. SANTAI B. MISSISSIPI

Learn how to calculate the number of distinct word arrangements from the letters of 'SANTAI' and 'MISSISSIPI'. This problem uses the permutation formula with repetition and applies combinatorics concepts. Suitable for Grades 10-12.

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