Multiple choice

Out of 6 consonants and 3 vowels, how many words can be formed considering exactly 3 consonants and exactly 2 vowels?

  1. 7200

  2. 3600

  3. 60

  4. 120
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A Correct answer
Explanation

Choose 3 consonants from 6: 6C3 = 20. Choose 2 vowels from 3: 3C2 = 3. Total combinations = 20 * 3 = 60. Arrange 5 letters: 5! = 120. Total words = 60 * 120 = 7200.

AI explanation

Using the combination formula, we choose 3 consonants from 6 in 6 C 3 ways, which equals 20, and 2 vowels from 3 in 3 C 2 ways, which equals 3. The total number of selections is 20 times 3 to give 60 sets of letters. Since each set of 5 letters can be arranged to form a word in 5 factorial ways, the total number of words is 60 times 120, which equals 7200.

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