Permutations and Combinations

Topics in this chapter

• Counting Principles and Factorials
• Linear Permutations
• Repeated-Object Arrangements
• Restricted Arrangement Techniques
• Combinations and Selection
• Role-Based Selection and Arrangement
• Circular Permutations
• Binomial Coefficients and Identities

Cheat sheet

Practice questions

1. Question 1Q-6783E4

   How many three-digit numbers can be formed using the digits 1, 2, 3, 4 and 5 without repetition?

   1. A.15
   2. B.30
   3. C.60
   4. D.125
   See the answer and solution
2. Question 2Q-5AD93F

   A committee of 3 members is to be selected from 5 boys and 4 girls. How many committees will contain at least one girl?

   1. A.50
   2. B.60
   3. C.74
   4. D.84
   See the answer and solution
3. Question 3Q-8FE7E2

   How many 5-digit even numbers can be formed using each of the digits 0, 1, 2, 3 and 4 exactly once?

   1. A.48
   2. B.60
   3. C.72
   4. D.96
   See the answer and solution
4. Question 4Q-3BE30E

   From 8 students, a captain and a vice-captain are to be chosen for a team. Explain whether this is a permutation or a combination and find the number of possible selections.

   See the answer and solution
5. Question 5Q-BB8123

   How many distinct arrangements can be made using all the letters of the word BANANA?

   1. A.20
   2. B.60
   3. C.120
   4. D.360
   See the answer and solution