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How many words can be formed from the letters of the word “DAUGHTER” so that the vowels always come together? 

(a) 2880 

(b) 4320 

(c) 3600 

(d) 3200

1 Answer

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Best answer

(b) 4320

There are eight letters in the word “DAUGHTER” including three vowels (A, U, E) and 5 consonants (D, G, H, T, R) If the vowels are to be together, we consider them as one letter, so the 6 letters now (5 consonants and 1 vowels entity) can be arranged in 6P6 = 6 ! ways. Also corresponding to each of these arrangements, the 3 vowels can be arranged amongst themselves in 3 ! ways. 

∴ Required number of words = 6 ! × 3 ! 

= 6 × 5 × 4 × 3 × 2 × 1 × 3 × 2 = 4320.

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