Question

There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. What is the probability that a randomly chosen team has 3 or 4 girls?

Answer 1

There are \({6\choose 3}*{7\choose 7}\) ways of choosing 3 girls and 7 boys to form the team of 10 and \({6\choose 4}*{7\choose 6}\) ways of choosing 4 girls and 6 boys to form a team of 10.

The total number of teams of 10 that can be formed from 13 people is \(13\choose 10\)

So the probability of 3 or 4 girls in a 10-member team is
$$
\large
{6\choose 3}*{7\choose 7}+{6\choose 4}*{7\choose 6}\over {13\choose 10}
$$

Does this make sense?