Multiple choice

One of 7 consonents and 4 vowels, how many words of 3 consonents and 2 vowels can be formed?

  1. 25200

  2. 1050

  3. 21400

  4. none of these
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A Correct answer
Explanation

Choose 3 of the 7 consonants and 2 of the 4 vowels, then arrange the 5 selected letters. The count is C(7,3) x C(4,2) x 5! = 35 x 6 x 120 = 25200.

AI explanation

The number of ways to choose 3 consonants from 7 is 7C3, which equals 35, and the number of ways to choose 2 vowels from 4 is 4C2, which equals 6. The 5 selected letters can be arranged among themselves in 5! ways, which is 120. Multiplying these values gives 35 multiplied by 6 multiplied by 120, resulting in 25200 words.

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