volleyball only, 10 play basketball only and 6 play tennis only 4 play all the three games and equal number play two games only
(a) write out this information in cardinal form.
(b)illustrate this information in a Venn diagram
(c) find the number of women who play volleyball
(d) how many play exactly one game
Not sure just what "an equal number play two sports only" means, but if it means that 3x players play exactly two sports, then
you left out how many play volleyball only. If that number is v, and x play each pair of 2 sports only, then the number of students is
v+10+6+3x+4
(a) In cardinal form, the information can be written as follows:
- Number of people who play volleyball only: 10
- Number of people who play basketball only: 10
- Number of people who play tennis only: 6
- Number of people who play all three games: 4
- Number of people who play two games only: Equal number
- Number of people who play exactly one game: To be determined
(b) To illustrate this information in a Venn diagram, we can use circles to represent each game (volleyball, basketball, and tennis) and their respective subsets.
--------------------
| |
| Volleyball |
| Only (10) |
| |
---------------------
| |
| |
| |
| Volleyball |
| and Basketball |
| (To be |
| determined) |
| |
---------------------
| |
| |
| |
| |
|Volleball and Tennis |
| (To be determined) |
| |
---------------------
(c) To find the number of women who play volleyball, we add up the numbers of people who play volleyball only and those who play volleyball and basketball:
10 (volleyball only) + To be determined (volleyball and basketball) = To be determined.
(d) To find the number of people who play exactly one game, we need to subtract the number of people who play two or three games from the total number of players. However, the total number of players is not given, so this cannot be determined without that information.