In the word DAUGHTER, there are 3 vowels namely, A, U, and E, and 5 consonants namely, D, G, H, T, and R. Number of ways of selecting 2 vowels out of 3 vowels =`""^3C_2 = 3` Number of ways of selecting 3 consonants out of 5 consonants = `""^5C_2 = 3` Therefore, number of combinations of 2 vowels and 3 consonants = 3 × 10 = 30 Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways. Hence, required number of different words = 30 × 5! = 3600
Last updated at Jan. 13, 2022 by Teachoo
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