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 _____.

Step-by-step solution

Given, We have to make four letter word from UNIVERSE each consisting 2 vowels and 2 consonants, Now in UNIVERSE, we have, E, E, I, U, (Vowels) + N, R, S, V (Consonants) 2 different vowels +   2 consonants can be arrange in 3 C 2 · 4 C 2 · 4 ! = 3 × 6 × 24 = 432 ways C 2 3 is taken because of repetition of letter E