How many 4-letter code words (no letter repeated) can be formed using the letters of the word COMPUTER such that the word contains at least one vowel?

COMPUTER has 8 distinct letters: 3 vowels (O, U, E) and 5 consonants (C, M, P, T, R).

Total 4-letter arrangements from 8 distinct letters = 8×7×6×5 = 1680.

Arrangements using only consonants (no vowel) = 5×4×3×2 = 120.

At least one vowel = 1680 − 120 = 1560.

Tip: "At least one" with a small forbidden category is almost always easiest via the complement: total minus none.