There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 playexactly 2 sports and 4 play all three. How many students play none?
Give Explanation and write the formula.
Answer is 136
Class XI Ch 1 Sets
Answers
Answer:
total= a+b+c-(sum of exactly 2)- 2 * ( all three)+ none
230= 80+42+12-(32)-2*(4)+none
none = 136
Step-by-step explanation:
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Given,
Total students = 230
Students play football = 80
Students play soccer = 42
Students play rugby = 12
32 play exactly 2 sports and 4 play all three.
To find,
Students play none
Solution,
We will calculate the number of students who play none of the sports by the formula which is given below:
Total students = students play football + students play soccer + students play rugby - ( students who play exactly 2 sports) - 2×(students who play all three sports) + students who play none
Putting the values in the above formula:
We will get,
230 = 80 + 42 + 12 -(32) -2×4 + students who play none
Students who play none = 230-80-42-12+32+8
Students who play none = 136
Hence, the number of students who play none of the sports are 136.