A class contains 5 boys and 6 girls. The teacher is told that 3 of the students can go on a school trip, and selects them at random. What is the probability that 2 boys and 1 girls are selected?
so the total way to choose 3 students randomly from 11 results in
now the ways to get 2 boys out of 5 is
and 1 girl from 6
putting it all together
one way to think about these problems is to consider smaller spaces. For instance lets consider just 3 people composed of 1 girl and 2 boys. If we wanted to see about 1 girl and 1 boy we could iterate through and see the following
we see there is a
For the denominator we have 3 choose 2 which is 3. Thus we can decompose our combinations and bring them together as needed. If you get stuck sometimes it helps to use a toy example that helps show the correct path.