find number of different 5-letter arrangements of word that can be made from letters of word INDIA so that (1) all vowels occur together (2)all vowels do not occur together

Asked by  | 29th Jan, 2014, 04:40: PM

Expert Answer:

Hello Tabish, The word INDIA has 3 vowels I, N and I of which I is repeated twice. The word INDIA has 2 consonants N and D (1) For the first arrangement the vowels to occur together The 3 vowels can be arranged within themselves in three ways. namely, IIA, AII and IAI The two consonants and three vowels together can be arranged in 3! x 3 ways = 3 x 2 x 3 =18 different arrangements. (2) For the arrangement that all vowels do not occur together, = Total number of arrangements - the number of arrangements when all vowels are together. Total number of arrangements= 5!/2 (since I is repeating) = 120/2 = 60 Therefore 60 - 18 = 42 different arrangements.

Answered by  | 29th Jan, 2014, 05:22: PM

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