Question

out of 80 players 35 play cricket, 42 play hockey, 25 play football, 8 play both cricket and hockey, 10 play both cricket and football, 7 play both hockey and football, 3 play all the three games---(main Q) HOW MANY PLAYERS ARE PLAYING ONLY ONE GAME?---(options) {a}102 {b}80 {c}61 {d}63​

Answer 1

Answer:

61

Step-by-step explanation:

NONE

Answer 2

Given: out of 80 players 35 play cricket, 42 play hockey, 25 play football, 8 play both cricket and hockey, 10 play both cricket and football, 7 play both hockey and football, 3 play all the three game

To Find : HOW MANY PLAYERS ARE PLAYING ONLY ONE GAME

Solution:

n(C) = 35

n(H) = 42

n( F) = 25

n( H ∩ C)  = 8

n( C ∩ F)  = 10

n( H ∩ F)  = 7

n ( H∩F∩C) = 3

Only hockey = n(H) -  n( H ∩ C)  - n( H ∩ F)  + n ( H∩F∩C)

Only Cricket = n(C) -  n( H ∩ C)  - n( C ∩ F)  + n ( H∩F∩C)

Only Football = n(F) -  n( H ∩ F)  - n( C ∩ F)  + n ( H∩F∩C)

Hence PLAYING ONLY ONE GAME

= n(H) + n(C) + n(F)  - 2( n( H ∩ C) + n( H ∩ F) +   n( C ∩ F))  + 3n ( H∩F∩C)

= 42 + 35 + 25  - 2( 8 + 7 + 10) + 3(3)

= 102 - 50 + 9

= 61

Hence 61 Players are playing only one game.

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