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

Question

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 ________.

Smart Achievers · Accepted Answer

(432)

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

So, there are 4 vowels and 4 consonants.

When both vowels are different,

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

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 ________.

Ans.
(432)

Vowels are U, I, E, E and consonants are 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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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 ________.

Ans. (432) Vowels are U, I, E, E and consonants are N, V, R, S. So, there are 4 vowels and 4 consonants. When both vowels are different, Number of ways =C23×C24×4!=432

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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 ________.

Ans.
(432)

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

So, there are 4 vowels and 4 consonants.

When both vowels are different,

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