In how many distinct ways can the letters of the word SEEDS be arranged? ..... ways
Algebra and Trigonometry (MindTap Course List)
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Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter14: Counting And Probability
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Problem 4CC: a In solving a problem involving picking r objects from n objects, how do you know whether to use...
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![**Permutations of the Word "SEEDS"**
**Question:**
In how many distinct ways can the letters of the word SEEDS be arranged?
**Solution Box:**
[ ways ]
---
To solve the problem of finding the distinct arrangements of the word "SEEDS," consider the following:
1. **Count the Total Letters:** The word "SEEDS" consists of 5 letters.
2. **Identify Repeated Letters:** The letter 'S' appears twice, and the letter 'E' appears twice.
3. **Use the Formula for Permutations of Multisets:**
\[
\frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}
\]
where \(n\) is the total number of letters, and \(n_1, n_2, \ldots, n_k\) are the frequencies of the repeated letters.
For "SEEDS":
\[
\frac{5!}{2! \times 2!}
\]
4. **Calculate Factorials:**
- \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)
- \(2! = 2 \times 1 = 2\)
5. **Compute the Number of Distinct Arrangements:**
\[
\frac{120}{2 \times 2} = \frac{120}{4} = 30
\]
Thus, the letters of the word "SEEDS" can be arranged in 30 distinct ways.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0615f7c-3e91-45ec-8ebd-43a498fc758f%2Ff04dee15-0c92-402e-a999-943e14901cf7%2Fbb24e64_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Permutations of the Word "SEEDS"**
**Question:**
In how many distinct ways can the letters of the word SEEDS be arranged?
**Solution Box:**
[ ways ]
---
To solve the problem of finding the distinct arrangements of the word "SEEDS," consider the following:
1. **Count the Total Letters:** The word "SEEDS" consists of 5 letters.
2. **Identify Repeated Letters:** The letter 'S' appears twice, and the letter 'E' appears twice.
3. **Use the Formula for Permutations of Multisets:**
\[
\frac{n!}{n_1! \times n_2! \times \ldots \times n_k!}
\]
where \(n\) is the total number of letters, and \(n_1, n_2, \ldots, n_k\) are the frequencies of the repeated letters.
For "SEEDS":
\[
\frac{5!}{2! \times 2!}
\]
4. **Calculate Factorials:**
- \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)
- \(2! = 2 \times 1 = 2\)
5. **Compute the Number of Distinct Arrangements:**
\[
\frac{120}{2 \times 2} = \frac{120}{4} = 30
\]
Thus, the letters of the word "SEEDS" can be arranged in 30 distinct ways.
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