QJEEM23Ma174b: JEE Main 2023 Mathematics - Class 11 JEEM23Ma174b Solution: The number of 4-letter words, with or without meaning, each…

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

$\begin{aligned}& ={ }^3 C_2 \times{ }^4 C_2 \times 4 ! \\\\& ={ }^3 C_1 \times{ }^4 C_2 \times 24 \\\\& =3 \times 6 \times 24=432\end{aligned}$