Question

If you flip a coin $5$ times, what is the probability of getting exactly $3$ tails?

Answer 1

Use the binomial probability distribution.
Explanation:
Assuming a fair coin, there are $2^5=32$ different arrangements of heads and tails after $5$ flips.
Also, there are ${}^5{C}_3=\frac{5!}{3!2!}=10$ ways to get exactly $3$ tails.
$P$ (exactly $3$ tails) $=\frac{10}{32}=\frac{5}{6}$
Hope that helped