The Basic Rules of Counting

# Screens restaurants product rule 2 if an experiment

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Unformatted text preview: ner? #(screens) × #(restaurants) Product rule 2: if an experiment is performed in m stages, with n1 outcomes for the ﬁrst stage, and n2 outcomes for the second, REGARDLESS OF FIRST, . . ., and nm outcomes for the mth, REGARDLESS OF ALL PREVIOUS, then the total number of outcomes for the experiment is n1 n2 . . . nm Math 30530 (Fall 2012) Counting September 13, 2013 3 / 12 Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? Math 30530 (Fall 2012) Counting September 13, 2013 4 / 12 Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? n options for ﬁrst item, then n − 1 for second (regardless of what was chosen ﬁrst), then n − 2 for second, etc. So by product rule, ﬁnal count is n × (n − 1) × (n − 2) × . . . × 3 × 2 × 1 Math 30530 (Fall 2012) Counting September 13, 2013 4 / 12 Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? n options for ﬁrst item, then n − 1 for second (regardless of what was chosen ﬁrst), then n − 2 for second, etc. So by product rule, ﬁnal count is n × (n − 1) × (n − 2) × . . . × 3 × 2 × 1 Example: Finishing orders in race with 8 runners, no ties allowed? 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40, 320 Math 30530 (Fall 2012) Counting September 13, 2013 4 / 12 Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? n options for ﬁrst item, then n − 1 for second (regardless of what was chosen ﬁrst), then n − 2 for second, etc. So by product rule, ﬁnal count is n × (n − 1) × (n − 2) × . . . × 3 × 2 × 1 Example: Finishing orders in race with 8 runners, no ties allowed? 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40, 320 Notation: “n factorial” n! = n × (n − 1) × (n − 2) × . . . × 3 × 2 × 1 Math 30530 (Fall 2012) Counting September 13, 2013 4 / 12 Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? n options for ﬁrst item, then n − 1 for second (regardless of what was chosen ﬁrst), then n − 2 for second, etc. So by product rule, ﬁnal count is n × (n...
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## This note was uploaded on 01/31/2014 for the course MATH 30530 taught by Professor Hind,r during the Fall '08 term at Notre Dame.

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