Question

In a college of 100 students , 84 play football, 73 play cricket 62 play both football and hockey, 62 play both cricket and football, 58 play both cricket and hockey while 50 play all the three games. Assume every students play at least one game.
Find the number of students who play
(i) cricket only
(ii) football only
(iii) hockey only

Answer 1

Answer:

Step-by-step explanation:

Total students = 100.

From those

Football players= 84.

Cricket prayers= 73.

Both football and hockey players= 62.

Both Cricket and football players= 62.

Both cricket and hockey players =58.

And 50 plays all three game's.

Here given any one plays at least one game.

84 + 73 = 157.

Who plays only one game = 157.

And who plays both of 2 games = 62+62+58= 182.

Play all three games = 50.

Now

Cricket players only= ( 62+ 50)-73= 39.

Football players only= (62+50) -84= 28.

Hockey players only = (62 ÷ 2) = 31 and 50÷ 3= 16.66

Total hockey players = 33.

Total prayers = 100.

Cricket players =39.

Football players = 28.

Hockey players = 33.

Total = 39+28+33 = 100.