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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Question**: How many distinct arrangements of the letters in the word Mississippi are possible?
**Options**:
- A. 34,650
- B. 39,916,800
- C. 1152
- D. 7920
**Answer**: The correct answer is A. 34,650.
**Explanation**: To determine the number of distinct arrangements of the letters in the word "Mississippi", we use the formula for permutations of multiset:
\[
\text{Number of arrangements} = \frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}
\]
Where:
- \( n \) is the total number of letters.
- \( n_1, n_2, \ldots, n_k \) are the frequencies of the distinct letters.
For "Mississippi":
- Total letters, \( n = 11 \)
- Frequency of M = 1
- Frequency of I = 4
- Frequency of S = 4
- Frequency of P = 2
\[
\text{Number of arrangements} = \frac{11!}{1! \times 4! \times 4! \times 2!} = \frac{39916800}{1 \times 24 \times 24 \times 2} = 34,650
\]
Therefore, there are 34,650 distinct arrangements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98667a3b-04a1-4070-9e78-df323cc94aec%2F22898f75-f58b-49d8-81e8-e263b81751e4%2Fmk0pifs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question**: How many distinct arrangements of the letters in the word Mississippi are possible?
**Options**:
- A. 34,650
- B. 39,916,800
- C. 1152
- D. 7920
**Answer**: The correct answer is A. 34,650.
**Explanation**: To determine the number of distinct arrangements of the letters in the word "Mississippi", we use the formula for permutations of multiset:
\[
\text{Number of arrangements} = \frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}
\]
Where:
- \( n \) is the total number of letters.
- \( n_1, n_2, \ldots, n_k \) are the frequencies of the distinct letters.
For "Mississippi":
- Total letters, \( n = 11 \)
- Frequency of M = 1
- Frequency of I = 4
- Frequency of S = 4
- Frequency of P = 2
\[
\text{Number of arrangements} = \frac{11!}{1! \times 4! \times 4! \times 2!} = \frac{39916800}{1 \times 24 \times 24 \times 2} = 34,650
\]
Therefore, there are 34,650 distinct arrangements.
Expert Solution
Step 1: Given Information
Yes we show that the how many possible distinct arrrangements for the word 'Mississippi', by using permutation
There are total 11 letters with repititions.
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Solved in 3 steps with 1 images
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