# 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?

##### 1 Answer

#### Explanation:

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.