In how many different ways can the letters of the word ‘DIGEST’ be arranged so that the vowels are never… · ABC26GN5278

In the given word DIGEST, we take the vowels IE as one letter. Then, we can write it as DGST (IE). This word has 5 letters which can be arranged among themselves in 5 = (5 × 4 × 3 × 2 × 1) = 120 ways. The letters of IE can be arranged in 2 ways. ∴ Number of ways of arranging the letters of given word with vowels together = (120 × 2) = 240 ways. Number of ways of arranging all the letters of the given word = 6 = (6 × 5 × 4 × 3 × 2 × 1) = 720 ways. ∴ Number of ways of arrangements so that the vowels are never together = (720 – 240) = 480.