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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

Expert ยท 5.9k answers ยท 5k people helped

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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