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This overview introduces basic concepts of permutations and combinations, key elements in probability. Permutations refer to the arrangements of items where order matters, represented as nPr for differentiable items. Combinations consider selections where order does not matter, helping us understand grouped arrangements of items. We explore how to calculate permutations with distinguishable and identical items in various scenarios, paving the way for a deeper understanding of probability applications.
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Basic Probability Permutations and Combinations: Permutations: Each separate arrangement of all or part of a set of items. The number of permutations is the number of different arrangements in which items can be placed. change order → different arrangement → different permutations
Basic Probability Permutations and Combinations: • Permutations: a. A total of n distinguishable items to be arranged. R items are chosen at a time (r ≤ n). The number of permutations of n items chosen r at a time is written nPr. (example)
Basic Probability Permutations and Combinations: • Permutations: b. To calculate the number of permutations into class. A total of n items to be placed. n1 items are the same of one class, n2 are the same of the second class and n3 are the same as a third class. n1+n2+n3=n The number of permutations of n items taken n at a time: (example)
Basic Probability Permutations and Combinations: • Combinations: c. Similar to Permutations but taking no account of order. The number of combinations of n items taken r at a time: (example)
