Difference between revisions of "Combinatorics Challenge Problems"
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Answer: <math>(\frac{385}{1024})</math> | Answer: <math>(\frac{385}{1024})</math> | ||
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| + | ==Problem 8== | ||
| + | A frog sitting at the point <math>(1, 2)</math> begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length <math>1</math>, 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 <math>(0,0), (0,4), (4,4),</math> and <math>(4,0)</math>. What is the probability that the sequence of jumps ends on a vertical side of the square<math>?</math> (Source: AMC 12A 2020). | ||
Revision as of 11:00, 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).
