# If I flip a coin n times how many different combinations are there? For example if a coin is flippe

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.
You can still ask an expert for help

## Want to know more about Discrete math?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

britspears523jp
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.

Jackson Duncan
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.