How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Question:

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Solution:

There are 4 vowels and 4 consonants in the word INVOLUTE.

Out of these, 3 vowels and 2 consonants can be chosen in $\left({ }^{4} C_{3} \times{ }^{4} C_{2}\right)$ ways.

 

The 5 letters that have been selected can be arranged in $5 !$ ways.

$\therefore$ Required number of words $=\left({ }^{4} C_{3} \times{ }^{4} C_{2}\right) \times 5 !=4 \times 6 \times 120=2880$

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