Combinatorics Challenge Problems
Problem 1
How many distinguishable towers consisting of 
blocks can be built with 
red blocks, 
pink blocks, and yellow blocks?
Answer: 
Problem 2
How many ways are there to seat 
people around the circle if 
of them insist on staying together?(All people are distinct)
Answer: 
Problem 3
When fair sided dice are rolled, what is the probability that the sum of the numbers facing up top is 
?
Answer: (
)
Problem 4
How many different ways are there to buy fruits when the choices are apples, pears, and oranges?
Answer: 
Problem 5
Ms.Carr asks her students to read any 5 of the 10 books on a reading list. Harold randomly selects 5 books from this list, and Betty does the same. What is the probability that there are exactly 2 books that they both select? (Source: AMC 10B 2020).
