AII.12 The student will compute and distinguish between permutations and combinations. The states that if one decision can be The student will use problem solving, mathematical communication, Fundamental Counting Principle made ways and another can be made ways, then the two decisions mathematical reasoning, connections, and representations to n m can be made ways. nm Compare and contrast permutations and combinations. A permutation is the number of possible ways to arrange a group of Calculate the number of permutations of objects taken at a time. n r objects without repetition and when order matters (e.g., the outcome 1, Calculate the number of combinations of objects at a time. 2, 3 is different from the outcome 3, 2, 1 when order matters; therefore, n r both arrangements would be included in the possible outcomes). Use permutations and combinations as counting techniques to solve practical problems. A combination is the number of possible ways to select or arrange objects when is no repetition and order does not matter (e.g., the Calculate and verify permutations and combinations using a graphing outcome 1, 2, 3 is the same as the outcome 3, 2, 1 when order does not utility. matter; therefore, both arrangements would not be included in the possible outcomes).
AII.12 The student will compute and distinguish between permutations and combinations. The Fundamental Counting Principle states that if one decision can be made n ways and another can be made m ways, then the two decisions can be made nm ways. A permutation is the number of possible ways to arrange a group of objects without repetition and when order matters (e.g., the outcome 1, 2, 3 is different from the outcome 3, 2, 1 when order matters; therefore, both arrangements would be included in the possible outcomes). A combination is the number of possible ways to select or arrange objects when is no repetition and order does not matter (e.g., the outcome 1, 2, 3 is the same as the outcome 3, 2, 1 when order does not matter; therefore, both arrangements would not be included in the possible outcomes). The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Compare and contrast permutations and combinations. Calculate the number of permutations of n objects taken r at a time. Calculate the number of combinations of n objects r at a time. Use permutations and combinations as counting techniques to solve practical problems. Calculate and verify permutations and combinations using a graphing utility.
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