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

There are 8 letters in the word DAUGHTER including 3 vowels and 5 consonants. We have to select 2 vowels out of 3 vowels and 3 consonants out of 5 consonants.

$\therefore$ Number of ways of selection = ${}^3{C}_2{\times }^5{C}_3=3\times 10=30$

Now each word contains 5 letters which can be arranged among themselves in $5!$ ways. So, total number of words
= $5!\times 30=120\times 30=3600.$