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  4. A survey of 500 television viewers produced the following information, 285 watch football, 195 watch hockey, 115 watch basket-ball, 45 watch football and basket ball, 70 watch football and hockey, 50 watch hockey and basket ball, 50 do not watch any of the three games. The number of viewers, who watch exactly one of the three games are

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Q. A survey of $500$ television viewers produced the following information, $285$ watch football, $195$ watch hockey, $115$ watch basket-ball, $45$ watch football and basket ball, $70$ watch football and hockey, $50$ watch hockey and basket ball, $50$ do not watch any of the three games. The number of viewers, who watch exactly one of the three games are

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Solution:

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$a+e+f+g=285, \quad b+d+f+g=195$
$c+d+e+g=115, \quad e+g=45, f+g=70, d+g=50$
$a+b+c+d+e+f+g=500-50=450$
So $, a+f=240, b+d=125, c+e=65$
$a+e=215, b+f=145 ; b+c+d=165$
$a+c+e=255 ; a+b+f=335$
Solving we get
$b =95, c =40, a =190, d =30, e =25, f =50$
and $g =20$
Desired quantity $= a + b + c =325$