In the a sport camp, 65% children know playing the football,70%−in voleyball,75%−in basketball.What is least number of children who know playing all above three sport games? (Answer 10%)


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Question Number 104972 by 1549442205PVT last updated on 25/Jul/20

$In the a sport camp, 65 % children know$ $playing the football, 70 % - in voleyball, 75 % - in$ $basketball . What is least number of children who$ $know playing all above three sport games ?$ $(Answer 10 %)$
	Answered by mr W last updated on 25/Jul/20

	$s i m p l e w a y w i t h o u t u s i n g s e t t h e o r y :$ $N_{F} = c h i l d r e n p l a y i n g f o o t b a l l o n l y$ $N_{F, V} = c h i l d r e n p l a y i n g b o t h f o o t b a l l a n d v o l l e y b a l l$ $N_{F, V, B} = c h i l d r e n p l a y i n g a l l t h r e e s p o r t s$ $N_{F} + N_{F, V} + N_{F, B} + N_{F, V, B} = 65 . . . (i)$ $N_{V} + N_{F, V} + N_{V, B} + N_{F, V, B} = 70 . . . (i i)$ $N_{B} + N_{F, B} + N_{V, B} + N_{F, V, B} = 75 . . . (i i i)$ $i + i i + i i i :$ $N_{F, V, B} + 2 (N_{F} + N_{V} + N_{B} + N_{F, V} + N_{F, B} + N_{V, B} + N_{F, V, B}) - (N_{F} + N_{V} + N_{B}) = 210$ $N_{F, V, B} + 2 \times 100 - (N_{F} + N_{V} + N_{B}) = 210$ $N_{F, V, B} = 10 + (N_{F} + N_{V} + N_{B})$ $N_{F, V, B} ⩾ 10$ $i . e . a t l e a s t 10 % c h i l d r e n k n o w$ $p l a y i n g a l l t h r e e s p o r t g a m e s .$
	Commented by 1549442205PVT last updated on 25/Jul/20

	$Great! Thank you Sir!$
	Commented by Rasheed.Sindhi last updated on 25/Jul/20

	$S u p e r b! E l e g a n t! M r W S i r!$
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