Statistics with discrete mathAn upper-level math class has 13 students: 4 of them are females....
Statistics with discrete math
An upper-level math class has 13 students: 4 of them are females. Two of the females and four of the males live oﬀ campus. How many ways can a project group of three students be chosen so that it has two on-campus members and at least one female? Explain your answer
Answer & Explanation
13 students composed of 9 males, 4 females.
4 females composed of 2 on campus, 2 off campus.
9 males composed of 5 on campus, 4 off campus.
13 students composes of 7 on campus, 6 off campus.
Let's find the amount of groups that have two on campus members.
You need to pick 2 of the 7, so . Then you need one more from off campus, so
So the number of groups with two on campus members is
Now you need at least one female. So let's find all of the groups of 2 on campus members and no females, then eliminate that from the above group.
You need to pick 2 on campus males. There are 5 to choose from, so . Then you need one from off campus, so , giving you