In how many distinct ways can the letters of the word MEDDLES be arranged? ..... ways
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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12:
![In how many distinct ways can the letters of the word MEDDLES be arranged?
[ ways ]
---
To calculate the number of distinct arrangements of the word "MEDDLES," we first count the total number of letters and then account for any repeated letters.
1. Total letters in "MEDDLES": 7
2. Repeated letters:
- D occurs 2 times
- E occurs 2 times
The formula for the number of distinct arrangements is:
\[
\frac{n!}{p1! \times p2! \times \ldots}
\]
where:
- \( n \) is the total number of letters.
- \( p1, p2, \ldots \) are the frequencies of the repeated letters.
Substituting in the values:
\[
\frac{7!}{2! \times 2!} = \frac{5040}{4} = 1260
\]
Thus, there are 1,260 distinct ways to arrange the letters of the word "MEDDLES."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0615f7c-3e91-45ec-8ebd-43a498fc758f%2F90d3ebd6-b02c-4931-93e6-a050b5609005%2F2ze9qf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In how many distinct ways can the letters of the word MEDDLES be arranged?
[ ways ]
---
To calculate the number of distinct arrangements of the word "MEDDLES," we first count the total number of letters and then account for any repeated letters.
1. Total letters in "MEDDLES": 7
2. Repeated letters:
- D occurs 2 times
- E occurs 2 times
The formula for the number of distinct arrangements is:
\[
\frac{n!}{p1! \times p2! \times \ldots}
\]
where:
- \( n \) is the total number of letters.
- \( p1, p2, \ldots \) are the frequencies of the repeated letters.
Substituting in the values:
\[
\frac{7!}{2! \times 2!} = \frac{5040}{4} = 1260
\]
Thus, there are 1,260 distinct ways to arrange the letters of the word "MEDDLES."
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