Question

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

Answer 1

Given : word DAUGHTER

To Find : ​ How many words with or without meaning, each of 2 vowels and 3 consonants can be  formed

Solution:

DAUGHTER

Vowels = A , U  E  = 3

Consonants = D  , G  H , T  , R  = 5

Number of  ways 2 vowels can be selected  =  ³C₂ = 3

Number of  ways 3 consonants can be selected  =  ⁵C₃ = 10

Total ways of selection = 3*10 = 30

Now 5 letters can be arranged in   5!   = 120 Ways

Total Words can be formed =  30 * 120 = 3600

3600  words with or without meaning, each of 2 vowels and 3 consonants can be  formed from the letters of the word DAUGHTER  ​

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