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**Plato** “HHHTTTTTT” that string represents tosses of a coin where we get four heads and six tails.

That **particular** string has the probability of $\displaystyle \left( {\frac{1}{2}} \right)^{10} $ of occurring.

If we rearrange that string in anyway, say “THTHTTHHT” it still represents four heads and six tails. There are $\displaystyle {{10} \choose 4} = \left( {\frac{10!}{(4!)(6!)}} \right)$ way to rearrange that string.

So there are that many ways to get four heads and six tails.

In the sum we did it for 0,1,2,3, & 4.