Difference between revisions of "2015 UNCO Math Contest II Problems/Problem 10"

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== See also ==
 
== See also ==
{{UNCO Math Contest box|year=2015|n=II|num-b=10|after=Last Question}}
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{{UNCO Math Contest box|year=2015|n=II|num-b=9|after=BONUS}}
  
 
[[Category:Intermediate Combinatorics Problems]]
 
[[Category:Intermediate Combinatorics Problems]]

Revision as of 03:11, 3 February 2015

Problem

$\begin{tabular}[t]{|c|c|c|c|}\hline

& & & &\hline
& & & &\hline

\end{tabular}$ (Error compiling LaTeX. Unknown error_msg)

(a) You want to arrange $8$ biologists of $8$ different heights in two rows for a photograph. Each row must have $4$ biologists. Height must increase from left to right in each row. Each person in back must be taller than the person directly in front of him. How many different arrangements are possible?


$\begin{tabular}[t]{|c|c|c|c|c|c|}\hline

& & & & & & \hline
& & & & & & \hline

\end{tabular}$ (Error compiling LaTeX. Unknown error_msg)

(b) You arrange $12$ biologists of $12$ different heights in two rows of $6$, with the same conditions on height as in part (a). How many different arrangements are possible? Remember to justify your answers.


(c) You arrange $2n$ biologists of $2n$ different heights in two rows of $n$, with the same conditions on height as in part (a). Give a formula in terms of $n$ for the number of possible arrangements.


Solution

See also

2015 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
BONUS
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions