There are $240$ students in class XI of a school, $130$ play cricket, $100$ play football, $75$ play volleyball, $30$ of these play cricket and football. $25$ play volleyball and cricket, $15$ play football and volleyball. Also catch students play atleast one of the three games. How many students play all the three games?

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Solution

Totl students= $240$
$A = 130$ play cricket, $B = 100$ play football, $C = 75$ play volleyball.
$30$ play cricket & football.
$25$ play volleyball & cricket.
$15$ play football & volleyball.
$∴ A \cup B \cup C = A + B + C - A \cap B - B \cap C - A \cap C + A \cap B \cap C 240 = 130 + 75 + 100 - 30 - 25 - 15 + A \cap B \cap C A \cap B \cap C = 240 - 235 = 5$

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Totl students=240A=130 play cricket, B=100 play football, C=75 play volleyball.30 play cricket & football.25 play volleyball & cricket.15 play football & volleyball.∴A∪B∪C=A+B+C−A∩B−B∩C−A∩C+A∩B∩C240=130+75+100−30−25−15+A∩B∩CA∩B∩C=240−235=5