Multiple choice

From 8 consonants and 4 vowels of the English alphabet, how many 4-letter words, with or without meaning, can be formed such that each consists of 3 consonants and 1 vowel?

  1. 224

  2. 1,736

  3. 3,376

  4. 5,376

  5. 7,736
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Choose 3 consonants from 8: C(8,3) = 56. Choose 1 vowel from 4: C(4,1) = 4. Total combinations = 56 * 4 = 224. Arrange the 4 letters: 224 * 4! = 224 * 24 = 5376.

AI explanation

We must select 3 consonants out of 8 and 1 vowel out of 4, and then arrange the resulting 4 letters. Using the combination formula, the number of ways to select the letters is 8C3 * 4C1 = 56 * 4 = 224. Because these 4 distinct letters can be arranged among themselves in 4! = 24 ways, we multiply the selections by the arrangements to get 224 * 24 = 5376.

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