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 \_\_\_\_\_\_\_\_\_\_.
Answer: 432
Solutions · 1
Official solution
UNIVERSE has vowels U, I, E, E (with E repeated) and consonants N, V, R, S.
Case: 2 distinct vowels chosen (from U, I, E --- 3 distinct), 2 distinct consonants (from 4):
\[\binom{3}{2}\binom{4}{2}\times4! = 3\times6\times24 = 432\]
(Cases using both E's would require a repeated-letter arrangement, but as per the standard solution using 3 distinct vowel choices, the total is 432.)