Mathematics - Permutation & Combination Question with Solution | TestHub

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 ${}^3{C}_2{·}^4{C}_2·4!=3\times 6\times 24=432$ ways

{${}^{3}C_2$ is taken because of repetition of letter E }