In how many ways can an answer key for a quiz be…

In how many ways can an answer key for a quiz be written if the quiz contains 3 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

This problem repeats another one in the library (at most with different numbers), so it's left out of browsing.

AQuA-RAT — Algebra Question Answering with Rationales (Ling et al., DeepMind, 2017) · train #12203