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 one of the three sports?
If these medals went to a total of 58 men and only 3 men got medals in all the three sports, how many received medals in exactly two of the three ... Example 34 - Chapter 1 Class 11 Sets
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Answer:
If these medals went to a total of 58 men and only 3 men got medals in all the three sports, how many received medals in exactly two of the three ... Example 34 - Chapter 1 Class 11 Sets
Solution :
Let,
V = set of students getting medals in volleyball
F = set of students getting medals in football
B = set of students getting medals in basket ball
We are given the following:
n ( V ) = 38,
n ( F ) = 15
n ( B ) = 20
n ( V U F U B ) = 58
n ( V ∩ F ∩ B ) = 3
Let,
a = Number of students getting medals in volleyball and football but not the basketball
b = Number of students getting medals in football and basketball but not volleyball
c = Number of students getting medals in basketball and volleyball but not football
So,
n ( V U F U B ) is as follows :
⇒ [ 38 - ( a + c + 3 ) ] + [ 15 - ( a + b + 3 ) ] + [ 20 - ( b + c + 3 ) ] + a + b + c = 58
⇒ 67 - ( a + b + c ) = 58
⇒ a + b + c = 9
∴ Number of players who received medals in exactly two of the three sports,
⇒ a + b + c
⇒ 9
∴ Number of players who received medals in exactly two of the three sports is 9 respectively.