Combinatorics Challenge Problems

Revision as of 10:33, 23 April 2020 by Shiamk (talk | contribs) (Problem 3)

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


Problem 4

How many different ways are there to buy $8$ fruits when the choices are apples, pears, and oranges?

Answer: $(45)$