l04_orsamprepl

l04_orsamprepl - Ordered Sampling with Replacement Reading:...

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02/02/2009 CS206 - Intro. to Discrete Structures II 1 Ordered Sampling with Replacement Reading: Ross, Ch 1., Sec. 4. Rosen, Ch 5., Sec. 4 Adapted from Detlef Ronneburger Monday, February 2, 2009
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02/02/2009 CS206 - Intro. to Discrete Structures II 2 Example 1 • How many 8-long passwords using lowercase + uppercase letters + digits? #lowercase + uppercase + digits = 26+26+10=62 password = (t 1 ,t 2 ,t 3 ,t 4 ,t 5 ,t 6 ,t 7 ,t 8 ), t i = position i n i = # symbols in i-th position = 62, 8 i ) #passwords = n 1 ¢ n 2 ¢ ¢ n 8 = 62 8 ¼ 2.18 10 14 Monday, February 2, 2009
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02/02/2009 CS206 - Intro. to Discrete Structures II 3 Example 2 • How many different outcomes are there of rolling a dice k times? k-roll = (d 1 ,d 2 ,d 3 ,…,d k ), d i – outcome of i-th rolling n i = number of outcomes of i-th rolling = 6 #k-roll = i=1 k n i = n 1 ¢ n 2 ¢ n 3 ¢ ¢ n k = 6 k E.g., k=3, #3-roll outcomes = 6 3 = 216 Monday, February 2, 2009
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02/02/2009 CS206 - Intro. to Discrete Structures II 4 Ordered Sampling with Repetition • Let there be n outcomes of task t, and let the task t
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l04_orsamprepl - Ordered Sampling with Replacement Reading:...

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