I'm not sure how to reason about this problem.
Say we toss 12 coins in a row. What is the probability that 7 of those tosses were heads, and five were tails?
I've tried thinking of it as the number of ways to pick 7 things out of 12 options: $ \frac{12}{7!\ (12-7)!} $. I thought this was most reasonable, but it's wrong.
I also considered thinking of it as the number of permutations of 7 things with 2 choices divided by the number of permutations of 12 things: $ \frac{2^7}{2^{12}} $.
I'm not very sure where to go from here. Thank you for the help!