Question

Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?

Answer 1

Correct Answer: 432

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
 

Answer 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.