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: 110, 14, 17, 21, 27, 29, 33
Section 5.2: 14, 5, 7, 11, 13, 15, 17, 21, 29, 31
Section 5.3: 16, 7, 9, 13, 17, 29
Section 5.4: 15, 11, 13, 31, 37
Section 5.5: 14, 5, 9, 11, 13, 15, 19, 25, 29, 31, 41, 51, 67...
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 Spring '14
 Probability, Probability theory, 48 52

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