Question

33.In a college, 240 students play cricket, 180 students play football,164 students play hockey ,42 play both cricket and football, 38 play both football and hockey,40 play both cricket and hockey and 16 play all the three games . If each student participate in atleast one game , then find
(i) the number of students in the college
(ii)the number of students who play only one game.​

Answer 1

Answer:

(i) the number of students in the college  = 480

(ii) the number of students who play only one game.​ = Need to find this

Step-by-step explanation:

Cricket = 240 = n(A)

Football = 180 = n(B)

Hockey = 164 = n(C)

both cricket and football = 42 = n(A∩B)

both football and hockey = 38 = n(B∩C)

both cricket and hockey = 40= n(A∩C)

all the three games = 16 = n(A∩B∩C)

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n(AuBuC) = n(A)+n(B)+ n(C)-n(AnB)-n(Anc)-n(BnC)+n(AnBnC)

n(AuBuC) = 240 + 180 + 164 - 42 - 40 - 38 + 16 = 480

Answer 2

Answer:

(i) the number of students in the college  = 480

(ii) the number of students who play only one game.​ = Need to find this

Step-by-step explanation:

Cricket = 240 = n(A)

Football = 180 = n(B)

Hockey = 164 = n(C)

both cricket and football = 42 = n(A∩B)

both football and hockey = 38 = n(B∩C)

both cricket and hockey = 40= n(A∩C)

all the three games = 16 = n(A∩B∩C)

-----------------------

n(AuBuC) = n(A)+n(B)+ n(C)-n(AnB)-n(Anc)-n(BnC)+n(AnBnC)

n(AuBuC) = 240 + 180 + 164 - 42 - 40 - 38 + 16 = 480