Math Problem Statement
How many three-letter "codes" can be made from the following 10 letters "FGHIJKLMNO" if repetition of letters is not allowed?
Solution
To determine how many three-letter "codes" can be made from the letters "FGHIJKLMNO" without repetition, follow these steps:
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Count the number of available letters:
The letters available are "FGHIJKLMNO", which gives us a total of 10 distinct letters. -
Determine the number of choices for each position in the code:
- For the first position, you can choose any of the 10 letters.
- For the second position, since repetition is not allowed, you have 9 remaining letters to choose from.
- For the third position, you have 8 remaining letters to choose from.
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Calculate the total number of possible codes:
Multiply the number of choices for each position:
So, there are 720 different three-letter codes possible when repetition is not allowed.
Would you like more details or have any questions?
Here are some related questions you might find interesting:
- How many four-letter codes can be made if repetition is not allowed?
- What if only vowels are allowed in the code, and repetition is not allowed?
- How many three-letter codes can be made if the first letter must be a consonant?
- How many three-letter codes can be made if exactly two letters must be the same?
- How does the total number change if you allow repetition for only the last letter?
Tip: When repetition is not allowed, the number of choices decreases with each position, making the calculation a simple product of descending numbers.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Formulas
Permutation formula: P(n, k) = n! / (n - k)!
Theorems
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Suitable Grade Level
Grades 9-12
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