Difference between revisions of "2015 AMC 8 Problems/Problem 4"
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− | The | + | ==Problem== |
+ | |||
+ | The Blue Bird High School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible? | ||
<math>\textbf{(A) }2\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad \textbf{(E) }12</math> | <math>\textbf{(A) }2\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad \textbf{(E) }12</math> | ||
+ | |||
+ | ==Solution== | ||
+ | There are <math>2</math> ways to order the boys on the end, and there are <math>3!=6</math> ways to order the girls in the middle. We get the answer to be <math>2 \cdot 6 = \boxed{\textbf{(E) }12}</math>. | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/Zhsb5lv6jCI | ||
+ | |||
+ | ==Video Solution 2== | ||
+ | https://youtu.be/4sUA1029D14 | ||
+ | |||
+ | ~savannahsolver | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC8 box|year=2015|num-b=3|num-a=5}} | ||
+ | {{MAA Notice}} |
Revision as of 09:42, 29 March 2022
Problem
The Blue Bird High School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?
Solution
There are ways to order the boys on the end, and there are ways to order the girls in the middle. We get the answer to be .
Video Solution
Video Solution 2
~savannahsolver
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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.