1. MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability 8.3 8.3.1

2. 8.3.2 Applications of Combinatorics to Probability Two cards are picked at random from a deck of playing cards. What is the probability that they are both kings? Method 1: Using the fundamental counting principle P(2 kings) = Method 2: Using combinations Number of ways of choosing 2 kings from 4 kings is 4 C 2. Number of ways of choosing 2 cards from 52 cards is 52 C 2. P(2 kings) = P(2 kings)

3. Method 3: Using permutations Number of ways of arranging 2 kings from 4 kings is 4 P 2. Number of ways of arranging 2 cards from 52 cards is 52 P 2. P(2 kings) = 8.3.3 Applications of Combinatorics to Probability [cont’d]

4. 8.3.4 Using Combinatorics to Calculate Probability 1. A committee of 4 is to be selected from a group of 7 women and 5 men. What is the probability that there will be at least 1 woman on the committee? Consider the compliment for these types of problems: P(at least 1 woman) = 1 - P(0 women) The number of ways of selecting 0 women and 4 men from the group is 7 C 0 x 5 C 4. The number of ways of selecting a committee of 4 from the group of 12 is 12 C 4. P(at least 1 woman) = 1 - P(0 women) = 1 - 0.010 = 0.99 The probability of at least 1 woman on the committee is 0.99.

5. 8.3.5 2. The 7 letters of the word KITCHEN are arranged randomly. What is the probability of an arrangement containing the letters KIT in a group but not necessarily in that order? The number of ways of arranging the letters of KITCHEN in any order is 7!. The number of ways of arranging the letters of KITCHEN containing the letter group KIT is 5! x 3!. P(event) = = 0.143 The probability of the arrangement containing the sequence KIT is 0.143. Using Combinatorics to Calculate Probability

6. Suggested Questions: Pages 385 and 386 1-5, 9-16, 11 ad, 12 ade, 13, 15 8.3.6