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Probability (5)

# 5 4 3 60 5p 3 5 3 distinguishable permutations

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Unformatted text preview: (n ! r )! (n ! r ) " (n ! r ! 1) " ... " 2 "1 The number of arrangements of 3 people in a line choosing from 5 people is 5! = 5 " 4 " 3 = 60 . 5P = 3 (5 ! 3)! Distinguishable Permutations of n objects where n1, n2, … nk are types of objects There are 11! 11 ! 10 ! 9 ! 8 ! 7 ! 6 ! 5 11 ! 10 ! 9 ! 7 ! 5 = = = 34650 possible distinguishable 1!! 4 !! 4 !! 2! 4 ! 3 ! 2 !1 ! 2 !1 1 arrangements of the letters in the word MISSISSIPPI. Combination of a group of r objects from a group of n objects without regard to order n! n " (n ! 1) " ... " 2 "1 = n Cr = (n ! r )! r ! (n ! r ) " (n ! r ! 1) " ... " 2 "1 " r " (r ! 1) " ... " 2 "1 There are 52 C5 = 52! 52 " 51 " 50 " 49 " 48 52 " 51 "10 " 49 " 2 = = = 2598960 (52 ! 5)! 5! 5 " 4 " 3 " 2 "1 1 Homework: Section 5.1: 1-10, 14, 17, 21, 27, 29, 33 Section 5.2: 1-4, 5, 7, 11, 13, 15, 17, 21, 29, 31 Section 5.3: 1-6, 7, 9, 13, 17, 29 Section 5.4: 1-5, 11, 13, 31, 37 Section 5.5: 1-4, 5, 9, 11, 13, 15, 19, 25, 29, 31, 41, 51, 67...
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