Multiple choice

How many words containing 3 consonants and 3 vowels can be formed using 8 consonants and 5 vowels?

  1. 403200

  2. 5600

  3. 407200

  4. None of these
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A Correct answer
Explanation

Choose 3 consonants from 8: 8C3 = 56. Choose 3 vowels from 5: 5C3 = 10. Total combinations = 56 * 10 = 560. Each combination has 6 letters, which can be arranged in 6! = 720 ways. Total words = 560 * 720 = 403,200.

AI explanation

First, select the 3 consonants from the 8 available and the 3 vowels from the 5 available, which gives 8C3 multiplied by 5C3, equal to 56 times 10 equal to 560. These 6 chosen letters can be arranged among themselves to form a word in 6 factorial ways, which is 720. Multiplying the selection combinations by the arrangement permutations gives 560 multiplied by 720, resulting in 403200.

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