In how many different ways can the letter of the word CHESTNUT is arranged so that vowels always occur together?
Number of letters in ‘CHESTNUT’ = 8 Number of vowels = (E, U) = 2! Number of consonants = (C, H, S, T, N, T) = 6!/2! Now, consider the number of vowels together as one and vowels can be arranged = 2! So total number of ways = (7!/2!) × 2! = 5040
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