I thought it was 15 because he only has 15 puzzles

CD #1 can be paired with any one of the 15 puzzles, so that is 15 trips.

CD #2 can be paired with any one of the 15 puzzles, so that is 15 more trips.

CD #3 can be paired with any one of the 15 puzzles, so that is 15 more trips.

Each of the 27 CDs can be paired with each of the 15 puzzles.

27x15=405 trips can be taken