Grade 9 Exam > Grade 9 Notes > Statistics & Probability > Worksheet (with Solutions): Counting, Permutations, and Combinations
Worksheet (with Solutions): Counting, Permutations, and Combinations
# Counting, Permutations, and Combinations - Grade 9 Worksheet
Section A: Multiple Choice Questions
Q1: A restaurant offers 4 appetizers, 6 main courses, and 3 desserts. How many different three-course meals can be ordered?
(a) 13
(b) 24
(c) 72
(d) 108
Q2: How many different ways can the letters in the word "MATH" be arranged?
(a) 4
(b) 12
(c) 24
(d) 16
Q3: In how many ways can 3 students be selected from a group of 8 students to form a committee?
(a) 24
(b) 56
(c) 336
(d) 512
Q4: A lock has a 4-digit code where each digit can be any number from 0 to 9. How many different codes are possible if digits can be repeated?
(a) 40
(b) 5,040
(c) 10,000
(d) 1,000
Q5: How many permutations are there of the letters in the word "BOOK"?
(a) 24
(b) 12
(c) 6
(d) 4
Q6: In how many ways can 5 people stand in a line?
(a) 5
(b) 25
(c) 60
(d) 120
Q7: How many ways can you choose 2 books from a shelf of 7 books?
(a) 14
(b) 21
(c) 42
(d) 49
Q8: A student must answer 4 questions out of 6 questions on a test. In how many ways can the student select the questions?
(a) 10
(b) 15
(c) 20
(d) 24
Section B: Fill in the Blanks
Q9: The Fundamental Counting Principle states that if one event can occur in \(m\) ways and another event can occur in \(n\) ways, then both events can occur in __________ ways.Q10: A permutation is an arrangement of objects where __________ matters.Q11: The notation \(n!\) is called __________ and means the product of all positive integers from 1 to \(n\).Q12: The number of permutations of \(n\) objects taken \(r\) at a time is denoted by __________ or \(_nP_r\).Q13: The formula for combinations is \(C(n,r) = \frac{n!}{r! \times __________}\).Q14: By definition, \(0!\) equals __________.Section C: Word Problems
Q15: A pizza shop offers 3 types of crust, 5 types of sauce, and 8 types of toppings. If a customer must choose one of each, how many different pizza combinations are possible?Q16: A committee of 4 people needs to be formed from a group of 10 people. How many different committees can be formed?Q17: How many different 5-letter arrangements can be made using the letters in the word "LEVEL"?Q18: A teacher needs to arrange 6 students in a row for a photograph. In how many different ways can this be done?Q19: A school council has 12 members. In how many ways can a president, vice president, and secretary be chosen from the council?Q20: A basketball coach must select 5 players from a team of 9 players to start the game. How many different starting lineups are possible?The document Worksheet (with Solutions): Counting, Permutations, and Combinations is a part of the Grade 9 Course Statistics & Probability.
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Apr 20, 2026 Last updated
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