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:

  1. Count the number of available letters:
    The letters available are "FGHIJKLMNO", which gives us a total of 10 distinct letters.

  2. 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.
  3. Calculate the total number of possible codes:
    Multiply the number of choices for each position: 10×9×8=72010 \times 9 \times 8 = 720

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:

  1. How many four-letter codes can be made if repetition is not allowed?
  2. What if only vowels are allowed in the code, and repetition is not allowed?
  3. How many three-letter codes can be made if the first letter must be a consonant?
  4. How many three-letter codes can be made if exactly two letters must be the same?
  5. 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