Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball.Of the total ,64 played both basketball and hockey , 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games.Find
i)how many played only only cricket,basketball and only cricket,only hockey,only basket ball?
ii)how many played at least one game?
iii)how many played only two games?
iv)how many do not play any of the 3 games?

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2014-10-21T00:21:16+05:30

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See the Venn diagram enclosed.

Only cricket and basket ball = 80 - 24 = 56
only cricket and hockey = 40 - 24 = 16
only hockey and basket ball = 64 - 24 = 40

played only cricket = 224 - 56 - 24 - 16 = 128
only hockey = 240 - 16 - 24 - 40 = 160
only basketball = 336 - 56 -24 -40 = 216

Those who played no games = 800 - 336 - 128 -16 - 160 = 160

played at least one game = total - who played no game = 800 - 160 = 640

two games only = 56 + 16 + 40 = 112   (numbers calculated above)

no games = 160 - calculated above

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