coin flips

Question

A coin is flipped once. If the result is a heads, the coin is flipped 4 more times, and the result (heads or tails) of each successive flip is noted. If the result is a tails, the coin is flipped 2 more times and the result of each successive flip is noted.
How many possible outcomes are in the sample space of this experiment?

Answer 1

As written, it sounds like the order of each flip matters (e.g., (H,H,T,H) ≠ (H,H,H,T)). Assuming this is the case, the number of possible outcomes is simply the number of possible permutations you can arrange "H" and "T" exactly four times plus the number of possible permutations you can arrange "H" and "T" exactly two times. The number of permutations is quite small, so it's more than feasible to write them out by hand and count. The better way would be to ask yourself "how many possible ways can the coin land on the first flip, how many possible ways can the coin land on the second flip,..." and then multiply each number (why does this work?).

 

Note: "H" denotes the result of heads and "T" denotes the result of tails