Difference between revisions of "Combinatorics Challenge Problems"
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Answer: <math>(\frac{5}{8})</math> | Answer: <math>(\frac{5}{8})</math> | ||
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+ | ==Problem 9== | ||
+ | There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other? (Source: AMC 12B 2020). | ||
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+ | Answer: <math>(13)</math> |
Revision as of 12:02, 23 April 2020
Contents
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:
Problem 7
A fair coin is tossed times, each toss resulting in heads or tails. What is the probability that after all tosses, that there were atleast heads?
Answer:
Problem 8
A frog sitting at the point begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length , and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices and . What is the probability that the sequence of jumps ends on a vertical side of the square (Source: AMC 12A 2020).
Answer:
Problem 9
There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other? (Source: AMC 12B 2020).
Answer: