I understand how the problem becomes "What is the probability of getting exactly 3 heads in 5 flips of a coin?
I don't understand how a total of 32 possible outcomes exist.
From Barron's SAT Subject test math level 2
[Math] “If 10 coins are to be flipped and the first 5 all come up heads, what is the probability that exactly 3 more heads will be flipped?”
probability
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Best Answer
At least you've avoided the cliffs of not understanding independence of coin tosses successfully. A total of $32=2^5$ outcomes exists because each of the five remaining coins might be heads or tails. Only $5\choose 3$ of these outcomes are "good", thus the probability in question is $\frac{5\choose 3}{2^5}=\frac5{16}$.