Question

The numbers of words with or without meaning, each of 3 vowels and 2 consonants that can be made from the letters of the word 'INVOLUTE' are

• A. 2800
• B. 2880
• C. 2900
• D. None of these

Answer 1

Answer: (B)

In the word 'INVOLUTE', there are 4 vowels, namely, I, $O,E,U$ and 4 consonants namely, $N,V,L$ and $T$.
The number of ways of selecting 3 vowels out of $4={}^4{C}_3=4$.
The number of ways of selecting 2 consonants out of $4={}^4{C}_2=6$
Therefore, the number of combinations of 3 vowels and 2 consonants is $4\times 6=24$.
Now, each of these 24 combinations has 5 letters which can be arranged among themselves in 5! ways. Therefore, the required number of different words is $24\times 5!=2880$.