Combinations confusion for coin flips 10 fair coins are tossed. How many outcomes have 3 Heads?
I'm supposed to solve it with combination C(10, 3). But...
How do you know it's a combination that will solve it? I'm not interested in what makes it a combination, instead of a permutation. I know the answer is (some #)/3^10 total outcomes. But what is your thought process that initially makes you think, "I need to use the (n!)/(k!(n-k)!) combination formula on it."? I can easily identify when to use combinations on every combination-required problem I've encountered except for coin tosses.
I've already looked at Ian's problem, but our confusion seems a little different:
Combinations and Permutations in coin tossing
I have no problems understanding any other permutation or combination problems, like the (common?) horse race ordering problem, or picking colored balls out of urns. But something about coin flip combinations just completely baffles me. It might have something to do with the 50/50 heads tails chance.

think about naming the order of the tosses ...  toss#1, toss#2 etc.
e.g. The number of ways of getting 3 heads when tossing 5 coins is the same as the number of ways of deciding which 3 of the 5 tosses came up heads
e.g. the choice ${2,4,5}$ corresponds to the sequence THTHH
the choice ${1,2,5}$ corresponds to the sequence HHTTH
so the number of sequences containing 3 heads =$\binom 52$
