Multiple choice

In how many ways can we form words containing 3 vowels and 2 consonants (without repetition), if we are given 5 vowels and 6 consonants?

  1. 18000

  2. 3000

  3. 150

  4. 750

  5. None of these
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A Correct answer
Explanation

Number of ways to choose 3 vowels from 5 is 5C3 = 10. Number of ways to choose 2 consonants from 6 is 6C2 = 15. Total combinations = 10 * 15 = 150. Arranging these 5 letters = 5! = 120. Total words = 150 * 120 = 18000.

AI explanation

Using the multiplication principle, we first find the number of ways to select the required letters from the given pool. We select 3 vowels from 5 available in 5C3 ways, which is 10, and 2 consonants from 6 available in 6C2 ways, which is 15. After selecting the 5 distinct letters, they can be arranged in 5 factorial ways, so the total number of words is 10 x 15 x 120 = 18000.

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