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MATH / Given 5 colors to choose from, how many ways can we color the four unit squares…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Given 5 colors to choose from, how many ways can we color the four unit squares of a 2×22\times 2 board, given that two colorings are considered the same if one is a rotation of the other? (Note that we can use the same color for more than one square.) [asy] draw(unitsquare); draw((.5,0)--(.5,1)); draw((0,.5)--(1,.5)); [/asy]
Plain-text mathematical notation (without MathML)
Given 5 colors to choose from, how many ways can we color the four unit squares of a 2×2 board, given that two colorings are considered the same if one is a rotation of the other? (Note that we can use the same color for more than one square.)
[asy]
draw(unitsquare);
draw((.5,0)--(.5,1));
draw((0,.5)--(1,.5));
[/asy]
Original LaTeX notation
Given 5 colors to choose from, how many ways can we color the four unit squares of a $2\times 2$ board, given that two colorings are considered the same if one is a rotation of the other? (Note that we can use the same color for more than one square.)
[asy]
draw(unitsquare);
draw((.5,0)--(.5,1));
draw((0,.5)--(1,.5));
[/asy]

level

Level 5

type

Counting & Probability

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Source and history

task_id
12456fa8-77f1-5b2f-b270-2d5391c0c384
task_key
counting~5fand~5fprobability--test--12456fa8-77f1-5b2f-b270-2d5391c0c384
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import