Question 534822: 62 Freshmen were interviewed about the classes they were taking this semester.
25 said they were taking science
24 said they were taking math
22 said they were taking English
7 said they were taking both science and math
9 said they were taking both science and English
7 said they were taking both math and English
2 said they were taking all three classes
How many students are not taking any science, math, or English?
How many students are taking exactly one of science, math, or English classes?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! I do these kind of problems with a Venn diagram
That is 3 interlocking rings with an area in the
center that is common to all 3 rings.
If you look at the separate areas, you see there are 7
The center common area is the key
That is the 2 students who take S, M, and E.
7 take M&E
7-2 = 5 take ONLY M&E
7 take M&S
7-2 = 5 take ONLY M&S
9 take E&S
9-2 = 7 take ONLY E&S
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4 areas are now accounted for
22 take E
22 - ( 7 + 2 + 5 ) = 8 take ONLY E
24 take M
24 - ( 5 + 2 + 5 ) = 12 take ONLY M
25 take S
25 - ( 7 + 2 + 5 ) = 11 take ONLY S
--------------------
Now all 7 areas are accounted for
Adding them all up:
12 + 11 + 8 + 7 + 5 + 5 + 2 = 50
So, 50 students are taking the 3 courses
62 - 50 = 12 students are not taking S,M, or E
8 take ONLY E
12 take ONLY M
11 take ONLY S
8 + 12 + 11 = 31 take only 1 of these courses
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