1-24 Counting These exercises involve counting.
Tennis Games A group of friends has reserved a tennis court. They find that there are ten different ways in which two of them can play a singles game on this court. How many friends are in this group?
The number of friends.
There are ten different ways in which two of them can play a singles game on the court.
A combination of objects from a set is any subset of the set that contains elements (without regard to order).
If a set has objects, then the number of combination of elements from the set is denoted as and is called the number of combination of objects taken at a time. Then,
The total number of friends who can play a singles game on the court is , therefore chosen at a time for the tennis court in different ways.
Substitute for and for in equation .
The number of ways in which two of them can play a single game on the court is .
Substitute for in the above expression and calculate the value of .
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