How many words with or without meaning each of two vowels with 3 consonants can be formed from the letters of the word of?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Show
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 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 Concept: Combination Is there an error in this question or solution?
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How many words of 3 consonants and 2 vowels can be formed?Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters.
How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word shoulder?Solution 1
Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways.
How many words with or without means each of the three vowels?ways
= 120 ways. |