sandy wrote:
Six students compete in a table tennis tournament. Each student plays each of the other students four times. What is the total number of games played in the tournament?
Drill 1
Question: 10
Page: 561
We can also solve this question without using any traditional counting methods.
Let A, B, C, D, E and F be the six students Each student plays each of the other students four times.So, for example, student A plays:
Student B 4 times
Student C 4 times
Student D 4 times
Student E 4 times
Student F 4 times
In other words, student A plays a total of
20 games.
Applying the same logic we can see that student B plays a total of
20 games, student C plays a total of
20 games, etc
There are
6 students altogether.
So the TOTAL number of games played = (
6)(
20) =
120At this point, we must recognize that every game has been counted TWICE.
For example, when student A played a game against student B, student A counted that as a game, and student B also counted that is a game.
To account for this duplication, we must divide
120 by 2 to get
60Answer: 60
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