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Question

how many 3-letter combinations can be formed using all the letters of the alphabet?

Asked By FrostyBlaze52 at

Answered By Expert

Alvin

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Solution By Steps

Step 1: Total Number of Letters

There are 26 letters in the alphabet.

Step 2: Number of Ways to Choose the First Letter

For the first letter, there are 26 choices.

Step 3: Number of Ways to Choose the Second Letter

After choosing the first letter, there are 25 letters left for the second letter.

Step 4: Number of Ways to Choose the Third Letter

After choosing the first and second letters, there are 24 letters left for the third letter.

Step 5: Total Number of 3-Letter Combinations

To find the total number of 3-letter combinations, multiply the choices for each position: 26 choices for the first letter, 25 for the second, and 24 for the third.

Final Answer

The total number of 3-letter combinations using all the letters of the alphabet is 15,600.

Key Concept

Permutations

Key Concept Explanation

Permutations involve arranging items in a specific order. In this case, the key concept is used to calculate the number of ways to arrange letters in a 3-letter combination from the alphabet.

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