Out of 600 students in a school, 125 played cricket, 220 played footba

1.	Out of 600 students in a school, 125 played cricket, 220 played football and 300 played hockey of the total, 28 played both hockey and football, 70 played cricket and football and 32 played cricket and hockey, 26 played all the three games. What is the number of students who did not play any game? (a) 240 (b) 169 (c) 259 (d) 171
Answer» (c) 259 Here, n (c) = 125, n (F) = 220, n (H) = 300 n (H ∩ F) = 28 , n (C ∩ F) = 70, n (C ∩ H) = 32 and n ( C ∩ F ∩ H) = 26 ∴ Number of students who did not play any game = n (C′∩ F′∩ H′) = n ((C ∪ F ∪ H)′) = n ( ξ) – n (C ∪ F ∪ H) = n ( ξ) –[n (C) + n (F) + n (H) – n( C ∩ F) – n ( H ∩ F) – n ( C ∩ H) + n (C ∩ F ∩ H)] = 800–[ 125+220 + 300 – 70 –28–32– 26] = 800 – 541 = 259

Out of 600 students in a school, 125 played cricket, 220 played football and 300 played hockey of the total, 28 played both hockey and football, 70 played cricket and football and 32 played cricket and hockey, 26 played all the three games. What is the number of students who did not play any game? (a) 240 (b) 169 (c) 259 (d) 171

Answer»

(c) 259

Here, n (c) = 125, n (F) = 220, n (H) = 300

n (H ∩ F) = 28 , n (C ∩ F) = 70, n (C ∩ H) = 32 and n ( C ∩ F ∩ H) = 26

∴ Number of students who did not play any game

= n (C′∩ F′∩ H′)

= n ((C ∪ F ∪ H)′)

= n ( ξ) – n (C ∪ F ∪ H)

= n ( ξ) –[n (C) + n (F) + n (H) – n( C ∩ F) – n ( H ∩ F) – n ( C ∩ H) + n (C ∩ F ∩ H)]

= 800–[ 125+220 + 300 – 70 –28–32– 26]

= 800 – 541 = 259