The members of three athletic teams in the certain school, 21 are in basketball team, 26 in hockey team and 29 in the football team.14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games how many members are there in all?

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The members of three athletic teams in the certain school, 21 are in basketball team, 26 in hockey team and 29 in the football team.14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games how many members are there in all?

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The members of three athletic teams in the certain school, 21 are in b...

There are three athletic teams in a certain school: basketball, hockey, and football. The given information is as follows:

- 21 students are in the basketball team.
- 26 students are in the hockey team.
- 29 students are in the football team.
- 14 students play hockey and basketball.
- 15 students play hockey and football.
- 12 students play football and basketball.
- 8 students play all three games.

To find out the total number of members in all three teams, we need to calculate the sum of the members in each team while accounting for the overlapping players.

Finding the Total Number of Members:

First, let's calculate the number of members in each team who are not overlapping with other teams:

- Number of basketball players: 21
- Number of hockey players (excluding basketball players): 26 - 14 = 12
- Number of football players (excluding basketball players): 29 - 12 = 17

Calculating the Overlapping Players:

Now, let's calculate the number of players who play two sports:

- Number of players who play hockey and basketball: 14
- Number of players who play hockey and football: 15
- Number of players who play football and basketball: 12

To find the number of players who play only two sports, we need to subtract the players who play all three sports (8) from the sum of the above three values:

14 + 15 + 12 - 8 = 33

Calculating the Total Number of Members:

To find the total number of members in all three teams, we need to add the number of players in each team that are not overlapping with other teams, and the number of players who play only two sports:

21 + 12 + 17 + 33 = 83

Answer:

There are a total of 83 members in all three athletic teams.

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