JEE Main 2023 (Online) 6th April Evening ShiftQuestion 1
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 $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$432$
Solution
Formulas used. (1) $\binom nr$ selections, $r!$ arrangementsStep 1 - Distinct letters. UNIVERSE: vowels U, I, E (3); consonants N, V, R, S (4). Step 2 - Select. $\binom32\binom42=3\cdot6=18$. Step 3 - Arrange. $4!=24$. Step 4 - Total. $18\cdot24=432$. Answer: 432