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# 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 January 2014, 4:40 PM
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 Expert 29th January 2014, 5:22 PM
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