Question

In Section X, there are 12 male students and 10 female

students. If 5 students are selected at random from section X, what
is the probability that at most 3 females are selected?

Answer 1

Answer: 17/19

Explanation:

The number of ways that
`i` females are chosen is
`\binom{12}{5-i} \cdot \binom{10}{i}`.

So, the number of ways to pick at most 3 females is
`\sum^(3)_(i=0) \binom{12}{5-i} \binom{10}{i}=23562`.

The total number of ways to pick 5 students is
`\binom{22}{5}`, so the required probability is
`\frac{23562}{\binom{22}{5}}=(17)/(19)`.