SOLUTION: Suppose we flip a fair coin four times. Give the probability of observing exactly two "heads" in these four coin flips.

T T T T

T T T H

T T H T

T T H H   (1)



T H T T

T H T H   (2)

T H H T   (3)

T H H H



H T T T

H T T H   (4)

H T H T   (5)

H T H H



H H T T   (6)

H H T H

H H H T

H H H H



P(2 heads) = 6/16 = 3/8 = 0.375





Another way: there are four chances to get two heads, and there are 2^4 possible outcomes:   P(2 heads) = 4C2 / 2^4 = 6/16



And of course:  4 places to put the first H times 3 places for the 2nd H, but we divide by 2! because we've overcounted (the H's are indistinguishable) so we get  (4*3/2!)/2^4 = 6/16