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
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the given information:
- The total number of members in the sports club is 79.
- 19 members play both Football and Volleyball.
- 29 members play both Tennis and Volleyball.
- n members play all three games.
- 2n members play exactly one game.
To find the total number of players who play Volleyball, we need to take into account those who only play Volleyball, as well as those who play Volleyball in addition to other sports.
To start, we know that 2n people play exactly one game. Since 2n members play only one game and there are three games in total, we can deduce that n members play all three games.
So, if we subtract 2n from the total number of members in the club, we get the count of members who play two or more games. Therefore, 79 - 2n members play two or more games.
Now, let's consider the overlapping scenarios. We know that 19 members play both Football and Volleyball, and 29 members play both Tennis and Volleyball. However, this counts those who play all three games twice.
To account for this overlap, we subtract n (the count of members who play all three games) from the sum of members playing Football and Volleyball (19) and members playing Tennis and Volleyball (29).
19 + 29 - n represents the count of members who play two sports but not all three.
Therefore, the total count of members who play Volleyball would be the sum of those who only play Volleyball (2n) and those who play multiple sports (19 + 29 - n):
Total Count of Volleyball Players = 2n + 19 + 29 - n
Simplifying this equation, we get:
Total Count of Volleyball Players = 48 + n
So, the number of people who play Volleyball altogether is 48 + n.