16. In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-
five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
2 answers:
Answer:
[tex[ two groups=-68+25+25+34 -6=10[/tex]
Step-by-step explanation:
For this case we have a diagram of the situation on the figure attached.
And for this case we can us the following rule from probability:
Or equivalently:
We know the total on this case total=68, the people for history is A=25, for math B=25 and for english C=34, and the people in all the groups 3, so we can replace:
And if we solve for the poeple in two groups we got:
[tex[ two groups=-68+25+25+34 -6=10[/tex]
Answer:
Step-by-step explanation:
Total number of students = 68
Let history = H
Maths = M
English = E
n(H) = 25
n(M) = 25
n(E) = 34
n(HnMnE) = 3
Total = n(H) + n(M) + n(E) - people in exactly two groups + 2(people in exactly 3 groups) + people in none of the groups
68 = 25 + 25 + 34 - people in exactly two groups - 6 +0
68 = 84 -6 - people in exactly two groups
68 = 78 - people in exactly two groups
People in exactly two groups = 78 - 68
= 10
OR
From the venn diagram, people in exactly two groups are represented by x, y and z
Total = 25 - x - y - 3 + 25 - x - z - 3 + 34 - y - z - 3 + x + y + z + 3
68 = 50 - x - 3 + 34 - y - z - 3
68 = 84 - 6 - x - y - z
68 = 78 - x - y - z
68 - 78 = - x - y - z
-10 = -(x + y + z)
x+y+z = -10/-1
x+y+z = 10
The number of students that registered for exactly two courses = 10
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