Question 27 A survey on 500 players revealed that 265 of them like volleyball, 242 like football, and 213 play cricket. 57 players play all three games, while 50 players play none of the games. What is the difference between the number of players who like only volleyball and those who like both football and cricket? 7
Answers
Step-by-step explanation:
all =500
265=volley ball
242=foot ball
213=cricket
57= all three games
50=no game like
difference between volleyball -football-cricket
difference some other =7
Answer:
he difference between the number of players who like only volleyball and those who like both football and cricket is 7
Step-by-step explanation:
From the above question,
To solve this question, we will use the formula of three sets,
That is,
n(A∪B∪C) = n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)n(A∪B∪C) = n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)
−n(A∩C)+n(A∩B∩C).
Also, we will use the formula for exactly one of the three games,
That is,
n(A) + n(B) + n(C − 2 [n (A∩B) + n(B∩C) + n(A∩C)] + 3n (A∩B∩C) n (A) + n(B)
+ n(C) −2 [n(A∩B) + n(B∩C) + n(A∩C)] + 3n(A∩B∩C).
By using these formulas, we can find the solution of both the parts of the question.
In this question, we are asked to find the number of viewers who watch all the three games and who watch exactly one of the three games. We have been given that from a survey of 500 viewers, 50 do not watch any of the three games and therefore the total number of viewers are 500 – 50 = 450. Now, let us consider football viewers as the part of set A, hockey viewers as the part of set B and basketball viewers as the part of set C. So, from the given information in the question, that is, 285 watch football, 195 watch hockey, 115 watch basketball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, we can say that,
n(A)=285n(A)=285
n(B)=195n(B)=195
n(C)=115n(C)=115
(A∩C)=45(A∩C)=45
(A∩B)=70(A∩B)=70
(B∩C)=50(B∩C)=50
Also, we have found out that the total viewers of game are 450. So, we can write it as n(A∪B∪C)=450......(vii)n(A∪B∪C)=450......(vii)
(i) Number of viewers who watch all the three games, that is n(A∩B∩C)n(A∩B∩C).
We know that for any three sets, we can apply the formula,
Total players = 500
265 Players = volley ball
242 Players = foot ball
213 Players = cricket
57 Players = all three games
50 Players = no game like
Difference between volleyball -football-cricket
Difference some other =7
For more related question : https://brainly.in/question/8840602
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