Multiple choice

How many words can be formed each having two consonants and one vowel out of five consonants and two vowels?

  1. 21

  2. 120

  3. 240

  4. 280

  5. 360
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need to select 2 consonants from 5 (5C2 = 10) and 1 vowel from 2 (2C1 = 2). Total combinations = 10 * 2 = 20. Each combination has 3 letters, which can be arranged in 3! = 6 ways. Total words = 20 * 6 = 120.

AI explanation

We first select 2 consonants from the 5 available using the combination formula 5 C 2, which gives 10 ways. Then we select 1 vowel from the 2 available using 2 C 1, which gives 2 ways. The total number of selections is 10 times 2 to equal 20 sets of letters. Each set of 3 letters can be arranged in 3 factorial ways, so the total number of words is 20 times 6, which equals 120.

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