Permutation and Combinations Test 15 Problems and Answers

Math A30 Concept A: Permutations and Combinations Test  Name: Date:

Mark:

Show work where possible. 1. Calculate. a) 5! d) 7C3

b) 4! 3!

c) 6P12

e) 6C4

2. Find the number of possible outcomes if you toss a coin and roll a dice. 3. Explain the difference between permutations and combinations. 4. How many ways can the letters of the word FORMAT be arranged? 5. How many ways can the letters of the word MATHEMATICS  be arranged? 6. You select a president and vice-president from a group of 5 students. Find the number of possible outcomes. 7. You must select a committee of 3 from 12 students. How many different committees can be formed? 8. How many 3-digit numbers are possible p ossible using the digits 0, 1, 4, 5, 7 and 9? 9. Find the number of combinations of 7 objects taking 2 at a time. 10. A class has 14 boys and 16 girls. The class has to elect one boy and one girl to be representatives on a committee. How many different ways can they select them?

11. How many arrangements of three types of flowers are there if  there are 6 types to choose from? 12. If a university student has to choose 2 science classes from 5 available science classes and 3 other classes from a total of 7 other  classes available, how many different groups of classes are there? 13. How many different ways can you have 1st, 2nd, 3rd, and 4th in a race with 10 runners? 14. How many ways can 7 people be arranged around a round table? 15. A license plate has 3 letters and 3 digits in that order. A witness to a hit and run accident saw the first 2 letters and the last digit. If  the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit? Solutions 1. a) 120

b) 144

c) 30

d) 35

e) 15

2. 12 3. Permutations are when order is important. Combinations are when order is not important. 4. 720

5. 4989600

6. 20

7. 220

8. 180

9. 21

10. 224

11. 20

12. 350

13. 5040

14. 720

15. 2600