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

Explanation

There are 3 vowels and 5 consonants in the word 'DAUGHTER'. No.of ways of selecting 2 vowels and 3 consonants from them
`=.^(3)C_(2) xx .^(5)C_(3) = (3!)/(2!1!) xx (5!)/(3!2!) = (5 xx 4xx 3xx 2!)/(2 xx 1xx 1xx 2!) = 30`
No. of ways of arranging these 5 letters
`= 5! = 120`
Therefore, total number of words
`= 30 xx 120 = 3600`