Difference between revisions of "2015 AMC 8 Problems/Problem 4"
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| − | The | + | ==Problem== |
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| + | 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 | + | There are <math>2! = 2</math> ways to order the boys on the ends, 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>. |
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| + | ==Video Solution (HOW TO THINK CRITICALLY!!!)== | ||
| + | https://youtu.be/srGyMofBMsE | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/Zhsb5lv6jCI | ||
| + | |||
| + | ==Video Solution 2== | ||
| + | https://youtu.be/4sUA1029D14 | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2015|num-b=3|num-a=5}} | {{AMC8 box|year=2015|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 15:53, 17 January 2024
Contents
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 ends, and there are 
ways to order the girls in the middle. We get the answer to be 
.
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
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. 
