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.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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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