How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from letter

English

Gujarati

Hindi

6.Permutation and Combination

medium

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

$2880$

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 $24 \times 5 !=2880$

Standard 11

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