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# Math OERWeek 9 Homework, Part A

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

- Nikolay Konstantinov

Answer every question. Try being nice to your eyes and posture by printing this page and working with pencil and paper. Then use the button at the bottom of the page to create a code by processing your answers. Copy-and-paste the code into an e-mail along with the answer to your short answer question.

Keep trying each homework assignment until you get 8 out of 10 or more.

1. At a restaurant, you can choose from 3 appetizers, 11 entrees, and 4 desserts. How many different three-course meals can you have?

3 × 11 × 4 3! × 11! × 4! (3 × 11 × 4)!
3 + 11 + 4 3! + 11! + 4! (3 + 11 + 4)!

2. A pianist wants to play five pieces at a recital. In how many orders can the pianist arrange these pieces in the program?

5 25 120 125

3. In how many ways can first, second, and third prizes be awarded in a contest with 175 contestants?

525 1,050 877,975 5,267,850 175!

4. A local pizza shop is having a Five Topping Special. In how many ways can 5 pizza toppings be chosen from 14 available toppings?

70 120 1,680 2,002 240,240

5. The serial number on a dollar bill consists of a letter, followed by eight digits and then a letter. How many different serial numbers are possible if the letters and digits cannot be repeated?

between 1 billion and 2 billion less than 1 billion
between 2 billion and 3 billion more than 3 billion

6. The serial number on a dollar bill consists of a letter, followed by eight digits and then a letter. How many different serial numbers are possible if the letters and digits can be repeated?

between 1 billion and 2 billion less than 1 billion
between 2 billion and 3 billion more than 3 billion

7. Two kids play a game involving flipping two coins and keeping score. In each round, they flip the coins one at a time. One kid gets a point whenever the first coin is heads, and the other kid gets a point whenever the second coin is heads. They are surprised when three consecutive rounds happen without any points. What is the chance that this happens?

0.8% 1.6% 2.4% 4.2% 8.3% 25%

8. With a shuffled normal deck of playing cards, what is the probability of a randomly chosen card being either a red card or less than (but not equal to) five? Consider aces to be less than five.

58% 65% 81% 85%

9. A hospital needs to hire people to be on-call to provide language interpretation services. The Venn diagram shows the languages requested last month. (An overlap shows where a patient could manage with either Italian or Spanish, for example). What is the probability that one interpreter who speaks Spanish and Chinese will be sufficient for the next interpretation request?

46% 53% 57% 65%

10. A group of atheletes consists of 12 people: 8 men and 4 women. What is the probability that a randomly selected team of 3 people would be all of one gender?

0.2% 0.5% 24% 27%