Permutations and Combinations Worksheet

Algebra 2 Name __________________________ Permutations and Combinations Worksheet Period _______ Date ______________

For the following problems, write the problem using permutation or combination, or the counting principle, or factorial notation. Then solve the problem.

1. You go to a restaurant where you can select one main course from 2 main-course choices, one vegetable from 2 vegetable choices, and one beverage from 2 beverage choices. How many different combinations can you order?

2. Jane has a 4-digit combination lock on her suitcase and has forgotten the combination. a. How many different possibilities are there for the combination? b. How many different possibilities are there for the

combination if no repetition is allowed?

c. If she knows that the first digit is a 5 and the second digit is prime, how many numbers must Jane try before the lock is sure to open?

3. Suppose two letters are chosen at random from the word ALGEBRA. What is the probability that the first letter is a vowel and the second letter is a consonant?

4. Nine people apply to go on a medicine-related field trip, but there is only room in the van for seven of them. In how many different ways could the group of seven making the trip be chosen?

5. Krispy Kreme sells 30 varieties of donuts, including their famous glazed donut. Suppose one of the stores decides to make sample boxes with 12 different donuts in each box. How many different sample boxes could be made?

6. You were trying to guess the phone number of your crush. You know the area code, but you have to guess the remaining seven digits. Assuming that none of the digits repeat, how many different phone numbers are you going to have to try before ensuring that you get the right one?

7. You are required to solve any four of the six problems on a quiz. a. How many different selections are possible? b. If each problem is multiple choice and has 5 choices each, what is the

probability that you’ll get those 4 problems correct just by guessing?

8. How many different committees of three members can be formed from a group of eight people?

9. Sure Lock Co. makes locks with 40 numbers printed on the dial. A lock is opened by dialing three different numbers in a certain order. How many different sequences are possible?

10. Suppose Sure Lock Co. changes its lock so that the order in which you dial the three different numbers doesn’t matter. How many different combinations would be possible?

11. In how many different ways can you arrange four songs on a CD?

12. A pizzeria offers 13 different toppings. Find the number of different kinds of pizza they could make using a. 4 toppings b. 7 toppings c. If only two toppings are chosen at random, what is the probability of choosing a Hawaiian Pizza (Canadian bacon and pineapple)?

13. Irving cannot remember the correct order of the five digits in his ID number. He does remember that the ID number contains the digits 1, 4, 3, 7, 6. What is the probability that the first three digits of Irving’s ID number will all be odd numbers?

14. Two students at IHS will be chosen for a TV interview. If there are 2000 students at the school: a. How many different selections are possible? b. If there are 200 students in the band, what’s the probability that 2 band

members were chosen to be on TV?

15. You get to pick 8 of your 12 favorite songs to put on a cd. How many ways can eight songs be arranged from a choice of 12 songs?

16. The combination for a lock consists of three different integers from 1 to 36, inclusive, in a particular order. How many three-integer codes are possible? Write the answer in permutation notation and factorial form, then find its value.

17. How many different 6-player starting squads can be formed from a volleyball team of 11 players? What is the probability that the captain is not one of the 6?

18. A club of students wants to select their officers by random drawing. There are 9 seniors, 5 juniors, and 6 sophomores in the club. Three names will be drawn. The first person chosen will be the president, the second will be the treasurer, and the third will be the secretary. What is the probability that all officers will be juniors?

19. Fifteen people report for jury duty – 12 women and 3 men. a. How many different 12-person juries can be chosen? b. What is the probability that the jury is all women?

c. What is the probability that the jury has 9 women and 3 men?

20. A standard deck of playing cards has 52 cards.

a. How many different 5-card poker hands could be formed? b. What is the probability of being dealt a four of a kind?

c. What is the probability of a flush (any 5 cards in the same suit)?