Difference between revisions of "Combinatorics Challenge Problems"

(Problem 1)
(Problem 1)
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How many distinguishable towers consisting of <math>8</math> blocks can be built with <math>2</math> red blocks, <math>4</math> pink blocks, and <math>2</math> yellow blocks?
 
How many distinguishable towers consisting of <math>8</math> blocks can be built with <math>2</math> red blocks, <math>4</math> pink blocks, and <math>2</math> yellow blocks?
  
Answer: (<math>420</math>)
+
Answer: <math>(420)</math>
  
 
==Problem 2==
 
==Problem 2==

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