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 (integer)
432
Solution
Given, word is UNIVERSE
<br/><br/>Here, vowels are E, I, U and consonants are N, R, S, V
<br/><br/>$\therefore$ Required number of 4-letters words, with or without meaning,
<br/><br/>each consisting of 2 vowels and 2 consonants
<br/><br/>$$
\begin{aligned}
& ={ }^3 C_2 \times{ }^4 C_2 \times 4 ! \\\\
& ={ }^3 C_1 \times{ }^4 C_2 \times 24 \\\\
& =3 \times 6 \times 24=432
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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