Intuitively I understand something like "10 choose 3" as someone holding out an opaque bag containing 10 different objects and asking me to put my hand in and then instructing me, "from the 10 choose 3". So it's asking, how many different ways are there of me doing that. Fair enough.
But in part of the MIT opencourseware the author uses the same "10 choose 3" to calculate the number of different 10-flip coin sequences there are with exactly 3 heads.
I can't see how to relate the coin flipping to my "choose objects from a bag" intuitive example. In the coin experiment, in what way is a coin-flip equal to one of the ten objects in the bag, and in what way is each of the three heads like one of the three objects I pull out? Can anyone help? thx.