A fourth grade teacher needs to select 3 students, including at least 1 girl and at least 1 boy, from her class to hand out programs at the upcoming spring concert. If there are 8 girls and 7 boys in her class, in how many different ways can she select the 3 students?
+57 Explanation:
There are 56 ways to choose 2 girls out of 8 and there are 7 ways to choose 1 boy out of 7.
Because we use the word "and", we multiply 56 by 7, and we get 392.
But then, there's the possibility that we choose 1 girl and 2 boys.
There are 8 ways to choose 1 girl out of 8 and there are 42 ways to choose 2 boys out of 7.
Again, we multiply due to the word "and", so we get 336
We can add 392 and 336 because we choose 2 girls and 1 boy OR 1 girl and 2 boys.
Finally, we get an answer of 728.
Solution #2:
You can choose 1 girl and 1 boy first.
There are 8 ways to choose 1 girl and 7 ways to choose 1 boy.
Now there are 13 students left and one more student needed to help.
There are 13 ways to choose 1 more student. Gender doesn't matter now as we already have 1 girl and 1 boy.
Now we multiply as we need to choose 1 girl, 1 boy, AND another student.
Once again, we get an answer of 728.
