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

Bernard Boyer

Bernard Boyer

Answered question

2022-07-15

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

suchonos6r

suchonos6r

Beginner2022-07-16Added 14 answers

Step 1
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 ( 7 2 ) . Then you need one more from off campus, so ( 6 1 )
Step 2
So the number of groups with two on campus members is
( 7 2 ) ( 6 1 ) = 126
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 ( 5 2 ) . Then you need one from off campus, so ( 4 1 ) , giving you
( 5 2 ) ( 4 1 ) = 40
126 40 = 86

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?