The number of words that can be formed out of the letters a,b,c,d,e,f taken 3 together each word containing atleast one vowel.
a)96 b)90 c)24 d)120 e)12
a)96 b)90 c)24 d)120 e)12
In future, please don't paraphrase questions - make sure you reproduce the exact wording. In this case we can understand what the question means, but sometimes inaccurate reproduction makes questions unanswerable. Further, please always provide the source.Pinku wrote:The number of words that can be formed out of the letters a,b,c,d,e,f taken 3 together each word containing atleast one vowel.
a)96 b)90 c)24 d)120 e)12
On to the question!
Each word must contain at least one vowel, so there are two possible cases:
1 vowel + 2 consonants; or
2 vowels + 1 consonant.
Case 1:
2C1 * 4C2 = 2 * (4*3/2) = 2 * 6 = 12 possible combinations of letters. However, we can rearrange those 3 letters in 3! = 6 ways. So, 12*6 = 72 possible words.
Case 2:
2C2 * 4C1 = 1 * 4 = 4 possible combinations of letters. However, we can rearrange those 3 letters in 3! = 6 ways. So, 4*6 = 24 possible words.
Either case is acceptable, so we ADD them together:
72 + 24 = 96... choose (A).
