Flipping a fair coin 21 times. The probability of getting 8 heads in any order is
$$p = \frac{21!}{8!(21-8)!}0.5^8(1-0.5)^{21-8} = 0.097$$
I get that the Binomial formula takes into account the different sequences in which the heads can occur during the 21 flips. But in any case, I would at least had expected the Binomial formula to give a value a bit closer to $0.5$.
The question is: What am I then calculating by $8/21 = 0.38$?