Multiple choice

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is

  1. $24800$
  2. $25100$
  3. $25200$
  4. $25400$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Choose 3 consonants from 7: 7C3 = 35. Choose 2 vowels from 4: 4C2 = 6. Total combinations = 35 * 6 = 210. Each combination has 5 letters, which can be arranged in 5! = 120 ways. Total words = 210 * 120 = 25200.

AI explanation

We first choose 3 consonants out of 7 and 2 vowels out of 4, which is done using the combination formula. The number of ways to select the letters is 7C3 times 4C2, giving 35 times 6, which equals 210 selections. Since each selected group of 5 letters can be arranged among themselves in 5! ways, the total number of words is 210 times 120. This results in 25200 possible words.

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