The 79 members of a spot club play at least one of the following games Tennis, Football and Volleyball. 19 play Football & Volleyball and 29 play Tennis & Volleyball, n play all the three games. 2n people , each play only one game. How many play Volleyball altogether.?
Plzzzz help me
py problem is all those 2n&n peopl
As you found, 31 play Football and Tennis. But there is no way to know how many play exactly which one sport. Clearly, n can be any multiple of 3.
For example, if n=3, then there are 6 people who play exactly one sport, but there's no way to know how those six are designated.
There must be some other piece of information relating the relative numbers for the one-sport players.
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the information given:
Let A be the set of people who play Football, B be the set of people who play Tennis, and C be the set of people who play Volleyball.
We are given the following information:
- 19 people play Football and Volleyball, which means A ∩ C = 19.
- 29 people play Tennis and Volleyball, which means B ∩ C = 29.
We also know that 2n people each play only one game. This means that each person is in exactly one of the sets A, B, or C. So, we can say that:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|
We are given that A ∩ B ∩ C = n. Plugging in the given values, we get:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + n
Since each person only plays one game, we can say:
|A ∪ B ∪ C| = 2n
Now, let's substitute in the given values:
2n = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + n
Simplifying, we get:
n = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C|
Since we know that A ∩ B ∩ C = n, we can rewrite the equation as:
n = |A| + |B| + |C| - n - |B ∩ C| - |A ∩ C|
Finally, we can substitute in the given values:
n = |A| + |B| + |C| - n - 29 - 19
Simplifying further:
2n = |A| + |B| + |C| - 48
Now we need to find |C|, the number of people who play Volleyball. Rearranging the equation, we get:
|C| = 2n + 48 - (|A| + |B|)
So, to find the number of people who play Volleyball, we need to know the values of |A| and |B|. Unfortunately, that information is not provided in the problem statement, so we cannot solve this problem with the given information.
Please provide any additional information if available or clarify the question further if possible.