Overlapping Sets ch 7 pg. 98

[dana.s.lewis]

I was confused with the 3-Set Venn Diagram problem. I was taught a different way and came out with a different number then the book. The strategy I used was the Total = Group 1 + Group 2 - Both + Neither. This prob states:
20 Marketing Team
30 Sales Team
40 Vision
5 workers both M&S
6 workers both S&V
9 workers both M&V
4 workers in all three (M,S,&V)

Using my formula I would add the three different groups; subtract those workers in both; and subtract the workers in all three groups twice because they would be counted twice.

Groups: 20 + 30 + 40 = 90
Both: 5+6+9= 20
All three: 2(4) = 8

From this I get
90-20-8= 62

The book gets 74. Can someone explain why. Thanks

[RonPurewal]

there's a big problem here: namely, you're taking a formula that applies exclusively to problems with two sets, and trying to extrapolate to problems involving three or more sets. so the short answer is, 'you can't use the formula for this problem, because the formula doesn't work on problems like this one'. sorry to disappoint you!

in case you have an exceptional level of mathematical curiosity, here's the analogous formula for three sets (which you have absolutely no reason whatsoever to commit to memory):
Total # = (# in none) + (# in A) + (# in B) + (# in C) - (# in both B and C) - (# in both A and C) - (# in both A and B) + (# in A, B, and C)

good times!