Math OER
Week 9 Homework, Part A

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%

Short Answer Questions:

Here are population pyramids for two countries, from the United Nations Data.

A. Do these graphs show us (i) how population grows over time, (ii) the number of people in different age categories, or (iii) the percentage of people in different age categories?

B. How is Mexico expected to change between 2017 and 2050? Describe some reasonable social and economic predictions.

C. How is Germany expected to change between 2017 and 2050? Describe some reasonable social and economic predictions.