Number of triangles formed
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There are 10 points in a plane and 4 of them are collinear.
Find the number of triangles formed by producing the lines resulting from joining the points infinitely in both directions (assuming no two lines are parallel).
I can see that there are 10C2-4C2=40 straight lines. If no two pairs of lines were concurrent we would have 40C3=9880 triangles. However, I do not know how to adjust for the concurrent lines. Any help/suggestions much appreciated.
combinatorics
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There are 10 points in a plane and 4 of them are collinear.
Find the number of triangles formed by producing the lines resulting from joining the points infinitely in both directions (assuming no two lines are parallel).
I can see that there are 10C2-4C2=40 straight lines. If no two pairs of lines were concurrent we would have 40C3=9880 triangles. However, I do not know how to adjust for the concurrent lines. Any help/suggestions much appreciated.
combinatorics
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
There are 10 points in a plane and 4 of them are collinear.
Find the number of triangles formed by producing the lines resulting from joining the points infinitely in both directions (assuming no two lines are parallel).
I can see that there are 10C2-4C2=40 straight lines. If no two pairs of lines were concurrent we would have 40C3=9880 triangles. However, I do not know how to adjust for the concurrent lines. Any help/suggestions much appreciated.
combinatorics
There are 10 points in a plane and 4 of them are collinear.
Find the number of triangles formed by producing the lines resulting from joining the points infinitely in both directions (assuming no two lines are parallel).
I can see that there are 10C2-4C2=40 straight lines. If no two pairs of lines were concurrent we would have 40C3=9880 triangles. However, I do not know how to adjust for the concurrent lines. Any help/suggestions much appreciated.
combinatorics
asked Aug 29 at 7:39
TryinHard
465
465
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2 Answers
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In the statement, "assuming no two lines are parallel" probably means that the
$$binom102-binom42+1=40$$
lines are distinct and pairwise concurrent. Then the number of triangles is $binom403=9880$.
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Actually, I think I was on the right track. The number of triangles eliminated for each of the 4 collinear points is 7C3=35 and the number of triangles eliminated from the 6 non-collinear points is 9C3=84.
Hence we eliminate 4*35+6*84=644 triangles, resulting in 9880-644=9236 triangles formed.
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
In the statement, "assuming no two lines are parallel" probably means that the
$$binom102-binom42+1=40$$
lines are distinct and pairwise concurrent. Then the number of triangles is $binom403=9880$.
add a comment |Â
up vote
1
down vote
In the statement, "assuming no two lines are parallel" probably means that the
$$binom102-binom42+1=40$$
lines are distinct and pairwise concurrent. Then the number of triangles is $binom403=9880$.
add a comment |Â
up vote
1
down vote
up vote
1
down vote
In the statement, "assuming no two lines are parallel" probably means that the
$$binom102-binom42+1=40$$
lines are distinct and pairwise concurrent. Then the number of triangles is $binom403=9880$.
In the statement, "assuming no two lines are parallel" probably means that the
$$binom102-binom42+1=40$$
lines are distinct and pairwise concurrent. Then the number of triangles is $binom403=9880$.
edited Aug 29 at 8:22
answered Aug 29 at 8:02
Robert Z
85.5k1055123
85.5k1055123
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up vote
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down vote
Actually, I think I was on the right track. The number of triangles eliminated for each of the 4 collinear points is 7C3=35 and the number of triangles eliminated from the 6 non-collinear points is 9C3=84.
Hence we eliminate 4*35+6*84=644 triangles, resulting in 9880-644=9236 triangles formed.
add a comment |Â
up vote
0
down vote
Actually, I think I was on the right track. The number of triangles eliminated for each of the 4 collinear points is 7C3=35 and the number of triangles eliminated from the 6 non-collinear points is 9C3=84.
Hence we eliminate 4*35+6*84=644 triangles, resulting in 9880-644=9236 triangles formed.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Actually, I think I was on the right track. The number of triangles eliminated for each of the 4 collinear points is 7C3=35 and the number of triangles eliminated from the 6 non-collinear points is 9C3=84.
Hence we eliminate 4*35+6*84=644 triangles, resulting in 9880-644=9236 triangles formed.
Actually, I think I was on the right track. The number of triangles eliminated for each of the 4 collinear points is 7C3=35 and the number of triangles eliminated from the 6 non-collinear points is 9C3=84.
Hence we eliminate 4*35+6*84=644 triangles, resulting in 9880-644=9236 triangles formed.
answered Sep 5 at 10:27
TryinHard
465
465
add a comment |Â
add a comment |Â
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