A group of students consists of 5 boys and 4 girls. We want to form a team of three students chosen from the students in this group.

a) What is the number of possible teams?

b) Is it true that less than $5 \%$ of the possible teams are made up entirely of girls?
This exercise tested the knowledge of the basics of counting. Choosing 3 students out of 9 is first choosing the first one (9 possibilities), then the second (8 possibilities), and then the third (7 possibilities), but doing so, each team is counted six times, because there are six ways to order the three members of the team: $A B C, A C B, B C A, B A C, C A B, C B A$. Therefore, the number of distinct teams that can be formed, without ordering the members of the team, is $: \frac{9 \times 8 \times 7}{6}=84$.

The number of teams consisting only of girls can be calculated in the same way, but we can also note that choosing 3 girls out of 4 is equivalent to choosing the fourth, who is not part of the team, so this offers four possibilities. Since 5% of 84 is strictly greater than 4, it is true that less than 5% of the possible teams consist only of girls.