## mathmath333 one year ago Counting question

1. anonymous

@ganeshie8

2. mathmath333

|dw:1440718821577:dw|

3. mathmath333

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

4. mathmath333

the lines are perpendicular to each other.

5. ChillOut

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

6. anonymous

I just know theres a ton

7. 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.

8. ChillOut

That would be my guess :)

9. mathmath333

n=4,b=6 ?

10. ChillOut

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

11. mathmath333

ok thanks

12. ChillOut

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

13. mathmath333

no

14. mathmath333

i m relying on u

15. ChillOut

All right then!