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Mathematics 16 Online
OpenStudy (mathmath333):

Counting question

OpenStudy (anonymous):

@ganeshie8

OpenStudy (mathmath333):

|dw:1440718821577:dw|

OpenStudy (mathmath333):

\(\large \color{black}{\begin{align} & \normalsize \text{Find the number of rectangles.}\hspace{.33em}\\~\\ \end{align}}\)

OpenStudy (mathmath333):

the lines are perpendicular to each other.

OpenStudy (chillout):

Begin by choosing two pairs of horizontal lines and two pairs of vertical lines so you can have a rectangle.

OpenStudy (anonymous):

I just know theres a ton

OpenStudy (chillout):

Let \(\left(\begin{matrix}a \\ 2\end{matrix}\right)\) be the number of vertical lines that can be picked, and \(\left(\begin{matrix}b \\ 2\end{matrix}\right)\) the number of horizontal lines that can be picked. For each pair of horizontal lines, there's a pair of vertical lines that will form a rectangle with them. Therefore you have \(\left(\begin{matrix}n \\ 2\end{matrix}\right)\)*\(\left(\begin{matrix}b \\ 2\end{matrix}\right)\) as the number of rectangles.

OpenStudy (chillout):

That would be my guess :)

OpenStudy (mathmath333):

n=4,b=6 ?

OpenStudy (chillout):

Yes. And sorry, meant to be "a" in the last line.

OpenStudy (mathmath333):

ok thanks

OpenStudy (chillout):

No problem, do you have an answer to the problem?

OpenStudy (mathmath333):

no

OpenStudy (mathmath333):

i m relying on u

OpenStudy (chillout):

All right then!

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