How many words can be formed from the letters of the word SIGNATURE so that the vowels always come together?
How many words can be formed from the letters of the word SIGNATURE so that the vowels always come together?
(a) 720 (b) 1440 (c) 3600 (d) 2880 (e) None of these
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(e) The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are considered as one letter, we have six letters which can be arranged in 6P6 ways ie 6! ways. Note that the four vowels can be arranged in 4! ways.
Hence required number of words
= 6! × 4!
= 720 × 24 = 17280
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