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**Answers are on the last slide.**

Review Answers are on the last slide.

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**1. A medical researcher needs 6 people to volunteer**

to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be chosen?

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**How many different 4-letter passwords can be**

formed from the letters A, B, C, D, E, F, and G if no repetition of letters is allowed?

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**The model of the car you are thinking of buying**

is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?

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**4. An ice-cream store sells 2 drinks (soda or milk shakes),**

in four sizes (small, medium, large, or jumbo), and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

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**5. Telephone numbers in the United States begin with**

3-digit area codes followed by 7-digit local telephone numbers. Area codes and local telephone numbers cannot begin with 0 or 1. How many different telephone numbers are possible?

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**6. You and 19 of your friends have decided to form an**

internet marketing consulting firm. The group needs to choose 3 officers – a CEO, an operating manager, and a treasurer. In how many ways can those offices be filled?

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**7. How many ways can you select 6 free videos**

from a list of 200 videos?

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**8. In a race in which there are 50 runners and no ties,**

in how many ways can the first three finishers come in?

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**9. A 3-person committee is needed to study ways to**

improving public transportation. How many committees could be formed from the 8 people on the board of supervisor?

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**In poker, a person is dealt 5 cards from a**

standard 52-card deck. The order in which you are dealt 5 cards does not matter. How many different 5-card poker hands are possible?

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**11. You are taking a multiple-choice test that has 5 questions**

11. You are taking a multiple-choice test that has 5 questions. Each of the questions has 3 choices, with 1 correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?

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**12. To win at LOTTO in the state of Florida, one must**

correctly select 6 numbers from a collection of 53 numbers (1-53). The order in which the selection is made does not matter. How many different selections are possible?

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**A die is rolled once. Find the probability of**

getting a number less than 5.

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**14. If you are dealt one card from a standard**

52-card deck, find the probability of being dealt the king of hearts.

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**15. Florida’s lottery game, LOTTO, is set up so that each**

player chooses six different numbers from 1 to 53. If the 6 numbers chosen match the 6 numbers drawn randomly twice weekly, the player wins (or shares) the top prize. With one LOTTO ticket, what is the probability of winning the prize?

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16. In 2001, Americans spent nearly 18 billion dollars on lotteries set up by revenue-hungry states. If a person buys 5000 different tickets in Florida’s LOTTO, (refer to previous problem), what is his probability of winning?

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**17. What is the probability of a family having 9 girls in**

a row?

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ANSWERS 1) ) ) 27 4) 40 5) 6,400,000,000 6) ) 8.24 x 10^10 8) 117,600 9) ) 2,598,960 11) ) 22,957, ) 2/3 14) 1/52 15) 1/22,957,480 16) 5000/22,957, ) 1/512

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3.7: Counting Objective: To find the counts of various combinations and permutations, as well as their corresponding probabilities CHS Statistics.

3.7: Counting Objective: To find the counts of various combinations and permutations, as well as their corresponding probabilities CHS Statistics.

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