Difference between revisions of "2014 AMC 8 Problems/Problem 16"

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<math>\textbf{(A) }60\qquad\textbf{(B) }88\qquad\textbf{(C) }96\qquad\textbf{(D) }144\qquad \textbf{(E) }160</math>
 
<math>\textbf{(A) }60\qquad\textbf{(B) }88\qquad\textbf{(C) }96\qquad\textbf{(D) }144\qquad \textbf{(E) }160</math>
==Video Solution==
 
https://youtu.be/Zhsb5lv6jCI?t=991
 
  
 
==Solution==
 
==Solution==
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Therefore, the total number of games is <math>56+32 = \boxed{88}</math>, so <math>\boxed{\text{(B)}}</math> is our answer.
 
Therefore, the total number of games is <math>56+32 = \boxed{88}</math>, so <math>\boxed{\text{(B)}}</math> is our answer.
 +
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==Video Solution 1 by OmegaLearn==
 +
https://youtu.be/Zhsb5lv6jCI?t=991
 +
 +
==Video Solution (CREATIVE THINKING)==
 +
https://youtu.be/G2Akf39uwcE
 +
 +
~Education, the Study of Everything
 +
 +
 +
==Video Solution 3==
 +
https://youtu.be/Zhsb5lv6jCI?t=991
 +
 +
https://youtu.be/w7Y-iq_kEaY ~savannahsolver
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=15|num-a=17}}
 
{{AMC8 box|year=2014|num-b=15|num-a=17}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 14:25, 29 September 2024

Problem

The "Middle School Eight" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays $4$ games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight" teams?

$\textbf{(A) }60\qquad\textbf{(B) }88\qquad\textbf{(C) }96\qquad\textbf{(D) }144\qquad \textbf{(E) }160$

Solution

Within the conference, there are 8 teams, so there are $\dbinom{8}{2}=28$ pairings of teams, and each pair must play two games, for a total of $28\cdot 2=56$ games within the conference.

Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of $4\cdot 8 =32$ games outside the conference.

Therefore, the total number of games is $56+32 = \boxed{88}$, so $\boxed{\text{(B)}}$ is our answer.

Video Solution 1 by OmegaLearn

https://youtu.be/Zhsb5lv6jCI?t=991

Video Solution (CREATIVE THINKING)

https://youtu.be/G2Akf39uwcE

~Education, the Study of Everything


Video Solution 3

https://youtu.be/Zhsb5lv6jCI?t=991

https://youtu.be/w7Y-iq_kEaY ~savannahsolver

See Also

2014 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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All AJHSME/AMC 8 Problems and Solutions

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