The Basic Rules of Counting

The Basic Rules of Counting

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Unformatted text preview: pears y times in x , then the correct count is x /y Math 30530 (Fall 2012) Counting September 13, 2013 5 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? Math 30530 (Fall 2012) Counting September 13, 2013 6 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? 10 6.5.4 = 25, 200 6 Math 30530 (Fall 2012) Counting September 13, 2013 6 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? 10 6.5.4 = 25, 200 6 What if John and Pat will not serve together, and Pat will only serve if Ellen is the chair? Math 30530 (Fall 2012) Counting September 13, 2013 6 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? 10 6.5.4 = 25, 200 6 What if John and Pat will not serve together, and Pat will only serve if Ellen is the chair? First consider committees with John (so without Pat), then those with Pat (so also with Ellen as chair, and without John), and then those without both John and Pat 8 7 8 6.5.4 + 5.4 + 6.5.4 = 10, 780 5 4 6 Math 30530 (Fall 2012) Counting September 13, 2013 6 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? 10 6.5.4 = 25, 200 6 What if John and Pat will not serve together, and Pat will only serve if Ellen is the chair? First consider committees with John (so without Pat), then those with Pat (so also with Ellen as chair, and without John), and then those without both John and Pat 8 7 8 6.5.4 + 5.4 + 6.5.4 = 10, 780 5 4 6 How many anagrams of MISSISSPPI? Math 30530 (Fall 2012) Counting September 13, 2013 6 / 12 Some examples How many ways can 10 people form a committee of 6, with a chair, a secretary a treasurer and 3 general members? 10 6.5.4 = 25, 200 6 What if John and Pat will not serve together, and Pat will only serve if Ellen is the chair? First consider committees with John (so without Pat), then those with Pat (so also with Ellen as chair, and without John), and...
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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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