Statistics with discrete mathAn upper-level math class has 13 students: 4 of them are females....

Bernard Boyer

Bernard Boyer

Answered

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

Expert

2022-07-16Added 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

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