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MATH 106 Lecture 2 Permutations & Combinations

11 MATH 106 Lecture 2 Permutations & Combinations m j winter FS20042 Player NumbersSuppose double digits are not allowed? You have one of each the numbers; you select two and iron them on. How many choices have you for one shirt?6 * 5 = 30 Shirts have 2-digit numbersSix possible digits: 0, 1, 2, 3, 4, 5 How many different numbers?6 possibilities for first digit; 6 for second6 6= 3623 Permutations - Order MattersThe number of ways one can select 2 items from a set of 6, with order mattering, is calledthe number of Permutations of 2 items selected from 6626 5 = 30 = PExample: The final night of the Folklore Festival will feature 3 different bands. There are 7 bands to choose from. How many different programsare possible?4 Calculating nPrSolution to band problem: 7P3= 7 6 5 = 210 This is not the same as asking How many ways are there to choose 3 bands from 7? Write out expressions for52P4 7P6= 52 51 50 49= 7 6 5 4 3 2 = 7 6 5 4 3 2 1 = 7!

5 9 Combinations: 7C3 • In our list of 210 sets of 3 professors, with order mattering, each set of three profs is counted 3! = 6 times. The number of distinct combinations of 3

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