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 .