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A 10-letter word is made up of 4 vowels and remaining consonants, out of which one consonant is twice present in the word. How many different words can be formed using the letters of the word, such that the vowels always come together?

A 10-letter word is made up of 4 vowels and remaining consonants, out of which one consonant is twice present in the word. How many different words can be formed using the letters of the word, such that the vowels always come together? Correct Answer 60480

The 4 vowels are considered as one letter

No. of consonants = 10 – 4 = 6

No. of letters to be arranged = 6 + 1 = 7, out of which 1 occurs twice

No. of ways of arranging these letters = 7!/2! = 2520

No. of ways of arranging 4 vowels = 4! = 24

∴ Required no. of words = 2520 × 24 = 60480

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