Lesson 73- Using Permutations and Combinations to Calculate Probabilities

Using Combination's:
Sample space is list of all possible ways (equally likely) to select 2 cards from 52 cards:

Number of unordered ways to select 2 cards from 52 cards:  52C2 = 1326
Number of unordered ways to select 2 aces:  4C2 = 6

P(both cards aces) =  4C2    =  1/ 221
                                 52C2

Using Permutations:
Number of ordered ways to select 2 cards from 52 cards: 52P2

Number of ways to select 2 aces: 4P2

P(both cards aces)= 4P2   = 1/221
                              52P2

Example 1:    Three prizes are awarded in a raffle. One hundred people hold a ticket each

a) what is the probability that Alice, Ben, and Concetta win first, second, and third prizes respectively?
* Order Does Matter*
   1      = 1.03 x 10^-6
100P3

b) What is the probability that Alice, Ben and Concetta are the 3 prize winners (though not necessarilyin that order)?
* Order Does Not Matter*
      1   =  6.18 x 10 ^ -6
100C3

* Order Does Matter* = Permutation       * Order Does Not Matter*= Combination