In a class of 20 students, you’re picking 5 of them. There are 7 boys and 13 girls in the class.
- How many outcomes have three girls and two boys?
- What is the probability of the outcome consisting of one girl and four boys?
As we’re talking about the composition of groups, and not how they’re ordered, this is an unordered set.
- In this case you’re not interested in specific boys or girls, only that there are three girls and two boys. That means you have a case where the order does not matter, which tells you that each outcome is a combination. That makes the number of outcomes that have three boys and two girls
- Since there’s an equally large probability of a random girl being chosen as a random boy being chosen, you can use uniform probability. The number of favorable outcomes becomes
The number of possible groups of five is
That makes the probability