How to resolve the set?

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How to resolve the set?

by Fokin » Tue Apr 27, 2010 5:53 pm
There is a following set:

There are 50 employees in the ABC company Of these, 22 have taken an accounting course, 15 have thaken a course in finance, and 14 have taken a marketing course.Nine of the emloyees have taken exactly two of those courses , and one employee has taken all three of the courses. How many of the 50 employees have taken none of the courses
A)0
B)7
C)10
D)11
e)26
Right answer c

I've tried to resolve in the following way :

1) 22+15+14-3-3-3+2= 44
2) 51 -44 = 7
Source: — Problem Solving |

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by liferocks » Tue Apr 27, 2010 6:20 pm
total number of people enrolled in at least one course
= 22+14+15 -1*(number of people in exactly 2 courses)-2*(number of people in all 3 courses)
=(22+14+15)-1*9-2*1
=51-9-2
=40
hence number of employees have taken none of the courses=50-40=10