I simply cannot wrap my head around this fact:
"A fair coin is no more likely to produce any specific 10-toss sequence than any specific other one, but it is about 250 times as likely to produce one with exactly 5 heads as it is to produce one with 10 heads."
The probability of getting a specified coin toss sequence of e.g. 10 tosses is 1/10, so getting a sequence like HHHHHHHHHH has the same probability like getting HTTTHTHHTH. BUT according to the text snippet above, the probability of getting a sequence with exactly 10 heads is smaller than getting a sequence with 5 heads.
Can someone please explain how this is possible? My intuition is failing me at this point, I understand both statements separately, but I have a hard time seeing how they are both true at the same time because for me P('HHHHHHHHHH') = P('sequence with exactly 10 heads') holds.
Maybe it helps if someone puts it in different words or mathematical terms? Thank you!