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 $={ }^{4} C_{2} \times{ }^{5} C_{3} \times 5 !$

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