Numerical: A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
We can represent the data using Venn diagram.
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3 men got all 3 medals, so n( A ∩ B ∩ C) will be 3. Thus put 3 in the region n( A ∩ B ∩ C)
Lets count of orange, blue & pink region be a, b & c. These people received exactly 2 medals.
The Purple region will be 35-a-b, since 38 people got medals in football. Total count for football circle is 38. Similarly grey region will be 12-a-c & Green will be 17-b-c
Now it is total that total 58 men received these medals. That is n( A ∪ B ∪ C) = 58
Or 58 =( 35-a-b) + a +( 12-a-c) + 3 + b +( 17-b-c) + c Or a + b + c = 9 Thus 9 people received 2 medals.
Thus we can say that 3 men received 3 medals, 9 men received 2 medals & 26 men received 1 medal.