 # If I flip a coin n times how many different combinations are there? For example if a coin is flippe veirarer 2022-06-27 Answered
If I flip a coin n times how many different combinations are there?
For example if a coin is flipped 3 times I know how to calculate all the possible outcomes. I don't understand how I reduce that count to only the combinations where the order doesn't matter.
I know there's 8 permutations but how do you reduce that count to 4? {HHH,TTT,HTT,THH}
I've tried thinking about the combinations formula with repetition, the product rule, the division rule.
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Step 1
It might be easier if you list the combinations in sequence according to how many tails there are: $\left\{HHH,THH,TTH,TTT\right\}.$.
Step 2
That is, start with all Hs and then for each successive element of the set, change one H to a T. When you finally have all Ts you're done.
Note that this set shows TTH where yours shows HTT, but since order does not matter, these are the same combination.

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Explanation:
If you toss a coin n times, the number of heads obtained can arrange from 0 to n. Since all of the remaining tosses must be tails (excluding unlikely events such as the coin standing on its edge), there are $n+1$ possible outcomes.

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