When she chooses a password, Eloise always uses exactly ten different characters…

When she chooses a password, Eloise always uses exactly ten different characters: five letters (A, B, C, D, and E) and five numbers (2, 3, 4, 5, and 6). Additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. How many different passwords conform to these rules?

AQuA-RAT — Algebra Question Answering with Rationales (Ling et al., DeepMind, 2017) · train #30486