How many words with or without meaning , each of 2 vowels and 3 consonants can be formed the letters of the DAUGHTER ?

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G Prasad

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Selecting 3 vowels out of 3 can be done in 3C2 ways = 3. Selecting 3 consonants out of 5 can be done in 5C3 ways = 10. So, total 30 possibilities. Now these 5 letters can be arranged in 5! ways = 120. Total words = 3600.
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I believe in clearing the concepts first

(3c2)*(5c3)*(5!)
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GMAT Math Expert

2 vowels can be selected from the 3 vowels (A, U and E) in 3C2 ways. 3 consonants can be selected from the 5 consonants (D, G, H, T and R) in 5C3 ways and after the selection, 2 vowels and 3 consonants can be arranged in 5! ways. So total number of ways = 3C2*5C3*5!
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In the word Daughter there are three vowels namely A, U, E and 5 consonants namely D, G, H, T and R. Number of ways of selecting 2 vowels out of 3 vowels = 3C2 = 3 Number of ways of selecting 3 consonants from 5 consonants = 5C3 = 10 Therefore, number of combinations of 2 vowels and 3 consonants =...
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In the word Daughter there are three vowels namely A, U, E and 5 consonants namely D, G, H, T and R. Number of ways of selecting 2 vowels out of 3 vowels = 3C2 = 3 Number of ways of selecting 3 consonants from 5 consonants = 5C3 = 10 Therefore, number of combinations of 2 vowels and 3 consonants = 3 x 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 x 5! = 3600 read less
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Spoken English, BTech Tuition, C Language, C++ Language, CAD etc., with 4 years of experience

3600
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Don't want to over express myself, just join and feel the experience.

3600
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Software Professional Trainer with 26+ years of Experience in Software Design and Development

3600
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rajni cv

3600
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Mathematics Teacher

(3p2)(5p3)=3!/1!.5!/2!=6.60=360
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