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How many rectangles can be formed by connecting the grid points from t

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MathRevolution
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How many rectangles can be formed by connecting the grid points from t [#permalink] New post   16 Jun 2019, 23:19
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E

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65% (hard)

Question Stats:

51% (02:00) correct 49% (02:38) wrong based on 67 sessions
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How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)

Attachment:
table 1.jpg
table 1.jpg [ 10.12 KiB | Viewed 2688 times ]


A. 72
B. 96
C. 108
D. 192
E. 315
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E
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chetan2u
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink] New post   17 Jun 2019, 03:37
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MathRevolution wrote:
How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)

Attachment:
table 1.jpg


A. 72
B. 96
C. 108
D. 192
E. 315



There are 7 vertical lines and 6 horizontal lines..
We require TWO of each to form a rectangle. 7C2*6C2=21*15=315

E
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jfranciscocuencag
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink] New post   17 Jun 2019, 16:17
chetan2u wrote:
MathRevolution wrote:
How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)

Attachment:
table 1.jpg


A. 72
B. 96
C. 108
D. 192
E. 315



There are 7 vertical lines and 6 horizontal lines..
We require TWO of each to form a rectangle. 7C2*6C2=21*15=315

E


Hello chetan2u!

I knew I had to do it like that, but my mistake was:

24C2

Why is it wrong with that?

Kind regards!
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chetan2u
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink] New post   17 Jun 2019, 18:49
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jfranciscocuencag wrote:
chetan2u wrote:
MathRevolution wrote:
How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)

Attachment:
table 1.jpg


A. 72
B. 96
C. 108
D. 192
E. 315



There are 7 vertical lines and 6 horizontal lines..
We require TWO of each to form a rectangle. 7C2*6C2=21*15=315

E


Hello chetan2u!

I knew I had to do it like that, but my mistake was:

24C2

Why is it wrong with that?

Kind regards!



24 C2 would mean choosing two points, which means you will get the possible number if lines by joining any two points. It will include diagonals etc.
For rectangle you have to choose 4 points. Now if you write it as 24C4, then these four points can be in one straight line, which will not result in a rectangle
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vargamartin1031
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink] New post   18 Jun 2019, 05:28
chetan2u wrote:
MathRevolution wrote:
How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)

Attachment:
table 1.jpg


A. 72
B. 96
C. 108
D. 192
E. 315



There are 7 vertical lines and 6 horizontal lines..
We require TWO of each to form a rectangle. 7C2*6C2=21*15=315

E


Hi chetan2u,

Can you explain this a bit more in detail? What do you mean by C?
Thanks
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MathRevolution
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink] New post   19 Jun 2019, 00:31
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Answer: E

Each collection of two horizontal and two vertical lines forms a rectangle. The number of ways to choose 2 vertical lines out of 7 lines is 7_C_2, and the number of ways to choose 2 horizontal lines out of 6 lines is 6_C_2.
Thus, the total number of rectangles is is 7_C_2 * 6_C_2.= [(7*6)/(1*2)][6*5]/(1*2)] = 21*15 = 315

Therefore, E is the answer.
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Re: How many rectangles can be formed by connecting the grid points from t [#permalink]
19 Jun 2019, 00:31
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