Multiple choice

Out of 7 consonants and 4 vowels, how many words can be made each containing 3 consonants and 2 vowels?

  1. 25200

  2. 2100

  3. 210

  4. 28

  5. 6
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A Correct answer
Explanation

Number of ways to choose 3 consonants from 7 is 7C3 = 35. Number of ways to choose 2 vowels from 4 is 4C2 = 6. Total combinations = 35 * 6 = 210. Each combination can be arranged in 5! = 120 ways. Total words = 210 * 120 = 25200.

AI explanation

To form the word, we first select 3 consonants out of 7 and 2 vowels out of 4, which gives 7C3 multiplied by 4C2 combinations. This evaluates to 35 multiplied by 6, yielding 210 selections. Each of these 5 selected letters can then be arranged among themselves in 5! ways, so we multiply 210 by 120. The result is 25200.

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