Difference between revisions of "Combinatorics Challenge Problems"

(Problem 2)
(Problem 3)
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Answer: <math>(36)</math>
 
Answer: <math>(36)</math>
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==Problem 3==
 
==Problem 3==

Revision as of 10:31, 23 April 2020

Problem 1

How many distinguishable towers consisting of $8$ blocks can be built with $2$ red blocks, $4$ pink blocks, and $2$ yellow blocks?

Answer: $(420)$


Problem 2

How many ways are there to seat $6$ people around the circle if $3$ of them insist on staying together?(All people are distinct)

Answer: $(36)$


Problem 3

When $6$ fair $6$ sided dice are rolled, what is the probability that the sum of the numbers facing up top is $10$?

Answer: ($\frac{7}{2592}$)