A fair coin is tossed three times. What is the probability it will land on heads exactly twice?
We know that flipping a single coin has two mutually exclusive outcomes, and that multiple flips constitute independent events.
This language suffices to explain why, for the trivial case of two coin flips, we can compute the odds of landing heads twice as P(H and H) = 1/2 x 1/2 = 1/4.
What other language can we use to describe the primary question? What are some attributes of probability problems that can be solved using the binomial coefficient?
I'm hoping that reading said language will develop my intuition as to why we apply n-choose-k to solve this problem.