Multiple choice

How many words can be formed by using 3 consonants and 2 vowels, if there are 5 consonants and 4 vowels are available to form words?

  1. 6200

  2. 7200

  3. 9200

  4. 7400

  5. 6400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Select 3 consonants from 5: 5C3 = 10. Select 2 vowels from 4: 4C2 = 6. Total combinations = 10 * 6 = 60. Arrange 5 letters: 5! = 120. Total words = 60 * 120 = 7200.

AI explanation

Using the combination formula, the 3 consonants can be chosen from 5 available in 5 C 3 ways, which equals 10. The 2 vowels can be chosen from 4 available in 4 C 2 ways, which equals 6. The total ways to select the 5 letters is 10 times 6, which equals 60, and these letters can be arranged in 5 factorial ways, giving 60 times 120 equals 7200.

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