Probability Counting - Counting Methods Counting outcomes...

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1 Counting Methods Counting outcomes in a Simple Sample Space Roll a pair of dice. Possible outcomes are 1,1 1, 2 1,3 1, 4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6 2 3 4 5 6 7 8 9 10 11 12 1234565 36 36 36 36 36 36 sum prob 4321 36 36 36 36 36
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2 Permutations of objects An arrangement of n distinct objects in a definite order is called a permutation of the n objects. How many different permutations are there? (choosefirst) (choose second) chooselast 11 nn .! Ans n
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3 Permutations The number of r -tuples we can make from n distinct objects is called the number of permutations of n things taken r at a time, denoted by nr P How many different r -tuples can you have? (choosefirst) (choose second) choose 11 th r n n −+ 0 ! . ( )! . 0! 1. ! and 1 nn n n Ans P note P n P = = = =
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4 94 Example. How many different ways are there to fill the first four batting positions from 9 players? 9, 4. 9! 3024 ways (9 4)! nr P = = = =
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5 Combinations The number of different ways of selecting elements out of distinct elements
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Probability Counting - Counting Methods Counting outcomes...

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