The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is

Step-by-step solution

There are 2 vowels and 4 consonants in the letters a, b, c, d, e, f . If we select one vowel, then number of arrangements = ^2 C₁ ^4 C₂ 3 !=2 4 3 2 3 2=72 If we select two vowels, then number of arrangements = ^2 C₂ ^4 C₁ 3 !=1 4 6=24 Hence, total number of arrangements =72+24=96