Multiple choice

The number of words which can be formed out of letters a, b, c, d, e, f taken 3 together, each containing one vowel atleast is

  1. $ ^2P_1 . ^4P_2 $

  2. 96
  3. $ ^6P_3 $

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total letters = 6 (a, b, c, d, e, f). Vowels = 2 (a, e), Consonants = 4 (b, c, d, f). Total ways to pick 3 letters = 6P3 = 120. Ways with no vowels = 4P3 = 24. Ways with at least one vowel = 120 - 24 = 96.

AI explanation

From the letters a, b, c, d, e, f, there are 2 vowels and 4 consonants, giving a total of 6 letters. The number of ways to form a 3-letter word with at least one vowel is found by subtracting the arrangements of only consonants from the total arrangements of any 3 letters. The total arrangements of 3 letters from 6 is 6P3, which equals 120, and the arrangements of 3 consonants from 4 is 4P3, which equals 24. Subtracting the consonant arrangements from the total gives 120 minus 24, which equals 96.

Keep practicing — related questions