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# Algebra II - Combinatorics: Help and Review Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. For each day of one school week, Mrs. Hudson gives her students a quiz in either math, science, or history. How many different combinations of quizzes are possible for the week?

#### Question 2 2. Calculate 4! (factorial)

#### Question 3 3. At Peter's Pizzeria, you can create your pizza choosing from 3 toppings, 3 cheese combinations, and 4 sizes. What are the events in this scenario?

#### Question 4 4. Mr. Garcia always dresses in a shirt, slacks, and dress shoes. There are 64 different outfits he can make with them. If he has 8 shirts and 2 pairs of shoes, then how many pairs of slacks does he have?

#### Question 5 5. Paul wants to play quarterback for his football team, but that decision depends on who serves as head coach for a given game. Coach Smith is head coach about 60 percent of the time, and Coach Brown is head coach the other 40 percent. Coach Brown has faith in Paul, so he starts him at quarterback in 80 percent of the games he coaches. Coach Smith, though, isn't so sure, so he starts Paul at quarterback 40 percent of the time. What's the probability of Paul starting as quarterback for the next game?

### Page 2

#### Question 6 6. The local bowling team plays in a 7-team league where each team plays other teams 4 times in a season. Using the combination formula, how many different games will be played in a season?

#### Question 7 7. Amanda has room in her rented limousine to take two of her friends while she celebrates her birthday. Her best friends are Barbara, Samantha, Rachel, and Kim. She chooses names randomly to not hurt anyone's feelings. What are the chances she'll take Rachel and Kim?

#### Question 8 8. Mrs. Jones has four children: two boys and two girls. How many different combinations of boys and girls could she have had and still have ended up with four children?

#### Question 9 9. Jane is attempting to unlock her locker but has forgotten her locker combination. The lock uses 3 numbers and includes only the numbers 1 to 9. Each of the digits also can not be repeated in the combination. How many possible locker combinations can be formed?

#### Question 10 10. All of the letters that spell MISSISSIPPI are put into a bag. What is the probability of selecting a vowel, and then after replacing the letter, also drawing an S?

### Page 3

#### Question 11 11. Solve 8! (factorial)

#### Question 12 12. How would you determine the total number of possible combinations in a situation using the fundamental counting principle?

#### Question 13 13. Using a standard deck of 52 cards, what is the probability of selecting a 4 and then after not replacing the card, selecting another 4?

#### Question 14 14. Solve 8! (the factorial of 8)

#### Question 15 15. Sam has to find one more pair of cards to win a memory game. Of the cards left, two show apples, two show oranges, and two show grapes. What are the odds of Sam turning over two cards and getting two cards with grapes?

### Page 4

####
Question 16
16.
Solve the expression 7*P*2 (*P* = permutation)

#### Question 17 17. Solve the following combination:

#### Question 18 18. If you roll a die three times, what is the probability of rolling only even numbers?

#### Question 19 19. A car lot has 50 Model A cars, 20 Model B cars, and 5 Model C cars. Joe has to sell 1 more Model A car and 1 more Model C car to get a bonus. What are the chances of this occurring if he sells only two more cars?

#### Question 20 20. Using a standard deck of cards (which has 26 red cards and 26 black cards, with 13 cards of every suit), what is the probability of selecting a red card, and then after replacing the card, selecting a heart card?

### Page 5

#### Question 21 21. Jimmy is making multi-flavored ice cream cones by scooping in different flavors one at a time. Jimmy has 6 different flavors but can only put 3 flavors in each cone. The order of the flavors is important to him as it affects how he tastes each ice cream. How many different arrangements of cones can Jimmy make?

#### Question 22 22. What are the odds of someone choosing a circle, a triangle, and a square in that order from the following group of shapes?

#### Question 23 23. Solve the following combination:

####
Question 24
24.
Solve the expression 5*P*4 (*P* = permutation )

#### Question 25 25. All of the letters of MISSISSIPPI are put in a bag. What is the probability of selecting an M and then after not replacing the letter, selecting a P?

### Page 6

#### Question 26 26. Solve the Combination

#### Algebra II - Combinatorics: Help and Review Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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