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).
Answer:
Problem 6*
points are chosen on the circumference of a circle to form a triangle. What is the probability that the circle does not contain the center of the circle?
Answer: