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Q.
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
Permutations and Combinations
Solution:
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 $24 \times 5 !=2880$.