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Combinatorics Challenge Problems

Revision as of 23:07, 22 April 2020 by Shiamk (talk | contribs) (Created page with "==Problem 1== 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>...")
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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})

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