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 ___________ . [2023]

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Solution

Q.
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 ___________ . [2023]

Ans.
(432)

$Vowels are U, I, E, E and consonants N, V, R, S$

$So, there are 4 vowels and 4 consonants.$

$When both vowels are different$

$∴$ $Number of ways = {}^{3}{C_{2}} \times {}^{4}{C_{2}} \times 4! = 432$

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