Let E denote the set of letters of the English alphabet, V = a , e , i , o , u and C be the complement of V in E . Then, the number of four-letter words (where repetitions of letters are allowed) having at least one letter from V and at least one letter from C is

Step-by-step solution

The number of all four-letter words = 26 4 The number of all four-letter words from set V = a , e , i , o , u i.e vowels = 5 4 Similarly, the number of all four-letter words from set of consonants = 21 5 ∴ Number of words which contains atleast one vowel and atleast one consonant = 26 4 - 21 4 - 5 4 = 26 2 + 21 2 26 2 - 21 2 - 5 4 = 676 + 441 5 47 - 5 4 = 5 1117 × 47 - 125 = 5 × 52374 = 261870