Difference between revisions of "2008 AMC 8 Problems/Problem 14"
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== Problem == | == Problem == | ||
− | Three <math>\text{A's}</math>, three <math>\text{B's}</math>, and three <math>\text{C's}</math> are placed in the nine spaces so that each row and column | + | Three <math>\text{A's}</math>, three <math>\text{B's}</math>, and three <math>\text{C's}</math> are placed in the nine spaces so that each row and column contains one of each letter. If <math>\text{A}</math> is placed in the upper left corner, how many arrangements are possible? |
<asy> | <asy> | ||
Line 15: | Line 15: | ||
== Solution == | == Solution == | ||
− | There are <math>2</math> ways to place the remaining <math>\text{As}</math>, <math>2</math> ways to place the remaining <math>\text{Bs}</math>, and <math>1</math> way to place the remaining <math>\text{Cs}</math> for a total of <math>(2)(2)(1) = \boxed{\textbf{(C)}\ 4}</math>. | + | There are <math>2</math> ways to place the remaining <math>\text{As}</math>, <math>2</math> ways to place the remaining <math>\text{Bs}</math>, and <math>1</math> way to place the remaining <math>\text{Cs}</math> for a total of <math>(2)(2)(1) = \boxed{\textbf{(C)}\ 4}</math>. |
− | + | ==Video Solution== | |
+ | |||
+ | https://www.youtube.com/watch?v=8qzMymleTIg ~David | ||
+ | |||
+ | ==Video Solution 2== | ||
+ | https://youtu.be/1m_c_iMvxKo Soo, DRMS, NM | ||
== See Also == | == See Also == | ||
{{AMC8 box|year=2008|num-b=13|num-a=15}} | {{AMC8 box|year=2008|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 21:28, 1 January 2024
Problem
Three , three
, and three
are placed in the nine spaces so that each row and column contains one of each letter. If
is placed in the upper left corner, how many arrangements are possible?
Solution
There are ways to place the remaining
,
ways to place the remaining
, and
way to place the remaining
for a total of
.
Video Solution
https://www.youtube.com/watch?v=8qzMymleTIg ~David
Video Solution 2
https://youtu.be/1m_c_iMvxKo Soo, DRMS, NM
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.