Math Problem Statement
Solution
The problem asks for the number of distinct arrangements of the 11 letters in the word "REINTERPRET", where identical letters are considered indistinguishable.
Step-by-Step Solution:
The word REINTERPRET consists of the following letter frequencies:
- R: 3 occurrences
- E: 3 occurrences
- I: 1 occurrence
- N: 1 occurrence
- T: 2 occurrences
- P: 1 occurrence
The formula for calculating the number of distinct arrangements of letters where some letters repeat is given by:
Where:
- is the total number of arrangements of 11 letters.
- The denominators , , , , , and account for the repeated letters (R, E, T, P, etc.).
Let's calculate it:
Thus, the number of distinct arrangements is:
Final Answer:
There are 554,400 distinct arrangements of the letters in "REINTERPRET".
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Related Questions:
- How do you calculate permutations of words with more than two identical letters?
- What if there were no repeating letters in "REINTERPRET"? How would the calculation change?
- Can the formula be applied to other words with different numbers of identical letters?
- How does the factorial operation scale as the word length increases?
- What is the significance of each step in simplifying the arrangement formula?
Tip: Always count the frequencies of each letter carefully before applying the formula to avoid errors in permutation problems.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations with Repetition
Formulas
n! / (k1! * k2! * ... * km!)
Theorems
Factorial Rule for Permutations with Repetition
Suitable Grade Level
Grades 10-12