JEE MAIN - Mathematics (2023 - 6th April Evening Shift - No. 16)
The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is __________.
Answer
432
Explanation
Given, word is UNIVERSE
Here, vowels are E, I, U and consonants are N, R, S, V
$\therefore$ Required number of 4-letters words, with or without meaning,
each consisting of 2 vowels and 2 consonants
$$ \begin{aligned} & ={ }^3 C_2 \times{ }^4 C_2 \times 4 ! \\\\ & ={ }^3 C_1 \times{ }^4 C_2 \times 24 \\\\ & =3 \times 6 \times 24=432 \end{aligned} $$
Here, vowels are E, I, U and consonants are N, R, S, V
$\therefore$ Required number of 4-letters words, with or without meaning,
each consisting of 2 vowels and 2 consonants
$$ \begin{aligned} & ={ }^3 C_2 \times{ }^4 C_2 \times 4 ! \\\\ & ={ }^3 C_1 \times{ }^4 C_2 \times 24 \\\\ & =3 \times 6 \times 24=432 \end{aligned} $$
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