Question:
Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?
Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?
Updated On: Feb 5, 2026
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Correct Answer: 432
Approach Solution - 1
The correct answer is 432
Vowels - I, U, E,
Consonants - N, V, R, S
⇒ 3C2 × 4C2 × 4!
= 3 × 6 × 24
= 432
So, 432 four letters word can be made
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Approach Solution -2
The word ""UNIVERSE"" consists of the vowels \(E, E, I, U\) and consonants \(N, V, R, S\).
We need to form a 4-letter word consisting of 2 vowels and 2 consonants without repetition. The calculation is as follows:
Case I: Two vowels different, 2 consonants different:
\[
\binom{3}{2} \cdot \binom{4}{2} \cdot 4! = (3) \cdot (6) \cdot (24) = 432
\]
Thus, the number of 4-letter words is 432.
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.