SOLUTION: In a group of 250 peoples 50 failed in mathematics 60 peoples failed in history and 70 peoples failed Geography 25 failed peoples failed mathematics and history and 28 peoples fail
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Question 1126097: In a group of 250 peoples 50 failed in mathematics 60 peoples failed in history and 70 peoples failed Geography 25 failed peoples failed mathematics and history and 28 peoples failed history and geography 32 failed mathematics and geography and 21 failed in all three subjects find the number of peoples who failed at least one subject? Answer by ikleyn(52794) (Show Source):
You are given 3 sets (the number of elements in three sets M, H and G);
You are given the numbers of elements in their in-pair intersections (M n H), (M n G) and (H n G);
and finally, you are given the numbers of elements in the triple intersection (M n H n G).
They ask you about the number of elements in the union of the three sets (M U H U G).
The same formula (*) works as in my previous post:
n(M U H U G) = n(M) + n(H) + n(G) - n(M n H) - n(M n G) - n(H n G) + n(M n H n G). (*)
you only need to substitute the given data and calculate:
n(M U H U G) = 50 + 60 + 70 - 25 - 28 - 32 + 21 = 116.
Answer. The number of peoples who failed at least one subject is 116.
Solved.
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This time I will not prove the formula (*) here: it is just proved under the referred link.
