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

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Text solutionVerified

Solution: vowels= I,O,U,E
consonants = N, V,L,T
total words

= (.^{4} C_{3} .^{4} C_{2}) .^{5} P_{5}

= \frac{4 !}{1 ! \cdot 3 !} \cdot \frac{4 !}{2 ! \cdot 2 !} \cdot \frac{5 !}{5 - 5}!

= 4 \cdot \frac{4 \cdot 3 \cdot 2}{4} \cdot 5!

= 24 \cdot 120

= 2880

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Question Text	How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Answer Type	Text solution:1
Upvotes	151