
Concept explainers
A soccer coach who has 12 children on her team will be playing 7 children at a time, each at a distinct position. Which of the following numbers is the largest? Explain your reasoning.
A)The number of permutations of the 7 positions that are possible with the 12 children. This number is 77, which is larger than the other two numbers.
B) The number of combinations of 7 children that can be chosen from the 12. This number is 12!(12−7)!, which is larger than the other two numbers.
C) The number of different ways of arranging the 7 children playing at any one time among the 7 positions. This number is 12!, which is larger than the other two numbers.
D) The number of combinations of 7 children that can be chosen from the 12. This number is 12!, which is larger than the other two numbers.
E) The number of permutations of the 7 positions that are possible with the 12 children. This number is 12!(12−7)!, which is larger than the other two numbers.
F) The number of different ways of arranging the 7 children playing at any one time among the 7 positions. This number is 77, which is larger than the other two numbers.

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