TA notes to Lecture 2.pdf - Econ 41 Kirill Ponomarev TA...

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Econ 41Kirill PonomarevTA Notes to Lecture 2Multiplication, Permutation and Combination rulesIn this course you will often need to calculate the total number of possible outcomes. There arethree fundamental rules in doing that.Multiplication ruleWhenever there is a number of consecutive steps, say,1,2, . . . , ?andat step?there are??possible options to choose from, the total number of options is given by:?1·?2·. . .·??Example 1(Shuffling).Suppose you have?songs in your music library.When you press“shuffle”, your phone or computer picks some random order.What is the total number ofplaylists that can be created in this way if there are no repetitions?
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Econ 41Kirill PonomarevPermutation ruleTo derive the total number of permutations with and without replacementwe just use the multiplication rule.First, let’s count permutations with replacement.Thenumber of ways to pick the first object is?. Since we put it back, the number of ways to pickthe second object is also?, and so on. In total we have?objects, sothe number of permutations

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