Emily is creating 3-letter combinations using 26 letters of the alphabet, where the middle letter must be a vowel, and both the first and third letters must be different consonants. How many unique combinations can she create?

Answer Choices

Correct answer marked below

1,800

1,900

2,000

2,100

Correct

2,300

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Official Explanation

Official

Let's denote the code as ABC. There are 5 vowels: a, e, i, o, u, which can occupy position B. Thus, there are 5 choices for B. For position A, we can choose any of the 21 consonants. Since A and C must be different and…

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Comments

AlejandroFeb 15, 2025

thank you taking time to upload it!

NiharikaJan 2, 2025

thanks a lot

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.