If a fair coin is tossed $8$ times, how many distinct outcome sequences (ordered head/tail outcomes) are possible?

Each toss has $2$ possible outcomes (H or T), and the tosses are independent. By the multiplication principle: $\underbrace{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2}_{8 \text{ tosses}} = 2^{8} = 256$. - Trap A ($16 = 2^{4}$) miscounts the number of tosses. - Trap B ($64 = 2^{6}$) is closer but still off. - Trap D ($362{,}880 = 9!$) confuses sequences-of-2-options with permutations of 9 objects. It is the ordered sequence that is counted — HHTHHTHT and HTHHTHTH are different outcomes even though both have 5 H and 3 T.