Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
Question:
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
Solution:
2 out of 4 vowels and 3 out of 5 consonants can be chosen in ${ }^{4} C_{2} \times{ }^{5} C_{3}$ ways.
The total number of letters is 5. These letters can be arranged in 5! ways.
$\therefore$ Total number of words $={ }^{4} C_{2} \times{ }^{5} C_{3} \times 5 !$