In how many 6-digit numbers do odd and even digits alternate (odd, even, odd, … or even, odd, even, …)?

Starting with an odd digit: every place has 5 choices, $5^6=15625$. Starting with an even digit: the first cannot be 0 (4 ways), the rest 5 each, $4\times 5^5=12500$. Total $15625+12500=28125$. (31250 lets 0 lead.)