Question 1175680: An automobile factory needs to select other companies as suppliers for 3 different parts. The factory contacted a number of companies and found that some companies produce 1 needed item, some produce 2, and others produce 3 needed items. 35 companies produce part A, 24 produce part B, and 27 produce part C. 12 companies produce both parts A and B, 19 produce part B and C, and 13 produce part A and C, and 9 produce all 3 parts. What was the total number of companies contacted?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Let X be the set of companies that produce item A;
Y be the set of companies that produce item B;
Z be the set of companies that produce item C.
You are given the numbers of elements n(X), n(Y), n(Z),
numbers of elements in all in-pair intersections n(XY), n(XZ), n(YZ);
and the number of elements in the triple intersection n(XYZ).
They want you find n(X U Y U Z).
Use the formula
n(X U Y U Z) = n(X) + n(Y) + n(Z) - n(XY - n(XZ) - n(YZ) + n(XYZ) =
= 35 + 24 + 27 - 12 - 19 - 13 + 9 = 51.
ANSWER. 51 companies were contacted.
Solved.
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