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# Permutations & Combinations in Probability 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. Annie writes the numbers 1 through 10 on note cards. She flips the cards over so she cannot see the number and selects three cards from the stack. What is the probability that she has selected the cards numbered 1, 2, and 3?

#### Question 2 2. Jimmy has the letters for the state of MISSISSIPPI written on cards, one letter per card. He turns the cards over and mixes up the order. If he selects one card at a time without replacing the cards, what is the probability that he will spell the word MISS in order?

#### Question 3 3. Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that boys will place 1st, 2nd, and 3rd in the marathon?

#### Question 4 4. Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that girls will place 1st, 2nd, and 3rd in the marathon?

#### Question 5 5. A locker combination contains four numbers between 1 and 20 and none of the numbers can be repeated. What is the probability that the locker combination will consist of all even numbers?

### Page 2

#### Question 6 6. Solve 8! (the factorial of 8)

#### Question 7 7. 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 8
8.
Solve the expression 5*P*4 (*P* = permutation )

####
Question 9
9.
Solve the expression 7*P*2 (*P* = permutation)

#### Question 10 10. 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?

### Page 3

#### Question 11 11. A newspaper company is selecting four houses to receive a free newspaper on your block. There are 10 houses on your block that are numbered 1-10. What is the probability that the four houses selected for a free newspaper will all be even numbered houses?

#### Question 12 12. At a local ice cream parlor, there are 6 different flavors of ice cream from which to select (strawberry, chocolate, vanilla, rocky road, mint chocolate chip, and peanut butter). Each ice cream sundae must include 2 different flavors of ice cream; what is the probability that the next customer's sundae will have vanilla and chocolate (in either order)?

#### Question 13 13. A class of 6 boys and 12 girls are preparing for finals. The teacher is going to select 3 students to be exempt from the test. What is the probability that the three students that are exempt will be all boys?

#### Question 14 14. Jane has cards with the letters ALABAMA on them. She lays the cards face down. What is the probability of Jane selecting two cards and both of them being a vowel?

#### Question 15 15. In Mr. Martin's math class there are 15 students out of which 4 will be selected to receive a special award. How many combinations of students can be selected?

### Page 4

#### Question 16 16. Calculate 4! (factorial)

#### Question 17 17. 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 18 18. Solve the following combination:

#### Question 19 19. Solve the following combination:

#### Question 20 20. Solve 8! (factorial)

### Page 5

#### Question 21 21. A hacker wants to find a customer's 5-digit PIN-code. How many different arrangements are there, given that the person who has the account may have used any given digit more than once when setting up the PIN-code?

#### Question 22 22. How many four-letter words, each consisting of four distinct letters (no repetitions of letters), can be formed using only the first seven letters of the alphabet?

#### Question 23 23. Tim and Joey have a toy train consisting of a single locomotive car and eight different carriages. In how many different ways can Tim and Joey form a train, keeping in mind that the locomotive car must be the first car in the train?

#### Question 24 24. How many different, six-letter arrangements can we form using the letters of the word 'person,' given that each arrangement must contain all six letters?

#### Question 25 25. At a charitable event, three raffle tickets are drawn from a total of 100, for first, second and third prizes. How many different ways are there for drawing the three winning tickets?

#### Permutations & Combinations in Probability 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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