In a group of children, 35 play football out of which 20 play football only, 22 play hockey; 25 play cricket out of which 11 play cricket only. Out of these 7 play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both.
(i) Number of player who play all the three games, is .
(ii) Number of player who play cricket and hockey but not football, is 
Text Solution
Verified by Experts(I) (5); (II) (2)
(i) (5) Given,
………. (i)
……………. (ii)
…………. (iii)
………. (iv)
……………. (v)
………. (vi)
……………. (vii)
………. (viii)
From Eqs. (vii), (viii) and (ix),
………. (ix)
From Eq. (vi), 
From Eq. (iii) 
Hence, 
Number of children play all the three games 
(ii) (2) Given,
…………. (i)
…………. (ii)
……. (iii)
……. (iv)
………. (v)
…………. (vi)
…………………. (vii)
…………………. (viii)
From Eqs. (vii), (viii) and (ix),
…………. (ix)
From Eq. (vi), 
From Eq. (iii) 
Hence, 
Number of children play cricket and hockey but not football
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