## mathmath333 one year ago On a board having 18 rows and 16 columns ,find the number of rectangles ?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ On a board having 18 rows and 16 columns ,find the number}\hspace{.33em}\\~\\ & \normalsize \text{ of rectangles ?}\hspace{.33em}\\~\\ \end{align}}

2. imqwerty

23256

3. mathmath333

18C2*16C2 ?

4. imqwerty

theres a formula to find it :D number of rectangles in an m x n grid can be given by - $\frac{ m(m+1)n(n+1) }{ 4 }$

5. mathmath333

no i want methos i cant remeber formula

6. mathmath333

*method,*remember

7. imqwerty

ok then try finding out the solution this way- How many ways can I draw two horizontal lines and two vertical lines through an array of (m+1) by (n+1) dots?

8. mathmath333

lol m confused

9. mathmath333

m+1C2*n+1c2

10. imqwerty

(Think of the dots formed at the corners of the little squares within the rectangle)

11. imqwerty

The two horizontal lines can be drawn C(m+1,2) ways, and the two vertical lines can be drawn C(n+1,2) ways, so the total number of rectangles within an m x n rectangle isC(m+1,2) C(n+1,2)

12. mathmath333

m+1C2*n+1C2 is correct ?