The usage of the term
arrangements is misleading. The prompt seems intended to ask the following:
Quote:
How many ways can 6 players be divided into pairs?
A. 10
B. 15
C. 25
D. 30
E. 40
The first player selected can be paired with any of the 5 other players.
Thus, the number of options for the first player selected =
5.
At this point, 4 players remain.
The next player selected can be paired with any of the 3 other players.
Thus, the number of options for the next player selected =
3.
The 2 remaining players must serve as the final pair.
To combine the options in blue, we multiply:
5*3 = 15.
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