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There are two parallel lines, one of the lines has 9 points on it and the other line has 10 points on it. What is the number of triangles that can be formed using these points only (as vertices)?
Correct answer is '765'. Can you explain this answer?
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Verified Answer
There are two parallel lines, one of the lines has 9 points on it and ...
To form a triangle, three points need to be selected. There are two options, either select 2 points from the line having 9 points and 1 point from the line having 10 points or 2 points from the line having 10 points and 1 point from the line having 9 points.
Number of triangles = 10C1 x 9C2 + 10C2 x 9C1 = 765
Answer: 765
Number of triangles = 10C1 x 9C2 + 10C2 x 9C1 = 765
Answer: 765
Most Upvoted Answer
There are two parallel lines, one of the lines has 9 points on it and ...
Introduction:
In this question, we are given two parallel lines, one with 9 points and the other with 10 points. We need to determine the number of triangles that can be formed using these points as vertices.
Approach:
To solve this problem, we can use the concept of combinations. We need to select 3 points from the given points on the lines to form a triangle. Since the two lines are parallel, we cannot select points from different lines to form a triangle. Hence, we need to consider all possible combinations of 3 points from each line separately.
Calculating the number of triangles on the line with 9 points:
To calculate the number of triangles on the line with 9 points, we need to select 3 points from these 9 points. This can be done using the combination formula. The number of ways to select 3 points from 9 points is given by:
C(9, 3) = 9! / (3! * (9-3)!) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 3 * 4 * 7 = 84
Calculating the number of triangles on the line with 10 points:
Similarly, to calculate the number of triangles on the line with 10 points, we need to select 3 points from these 10 points. Using the combination formula:
C(10, 3) = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 10 * 3 * 4 = 120
Total number of triangles:
Since the two lines are parallel, the triangles formed using points from each line are independent of each other. Hence, the total number of triangles that can be formed using these points is the product of the number of triangles on each line:
Total number of triangles = 84 * 120 = 10080
Conclusion:
Therefore, the correct answer is 10080, not 765 as mentioned.
In this question, we are given two parallel lines, one with 9 points and the other with 10 points. We need to determine the number of triangles that can be formed using these points as vertices.
Approach:
To solve this problem, we can use the concept of combinations. We need to select 3 points from the given points on the lines to form a triangle. Since the two lines are parallel, we cannot select points from different lines to form a triangle. Hence, we need to consider all possible combinations of 3 points from each line separately.
Calculating the number of triangles on the line with 9 points:
To calculate the number of triangles on the line with 9 points, we need to select 3 points from these 9 points. This can be done using the combination formula. The number of ways to select 3 points from 9 points is given by:
C(9, 3) = 9! / (3! * (9-3)!) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 3 * 4 * 7 = 84
Calculating the number of triangles on the line with 10 points:
Similarly, to calculate the number of triangles on the line with 10 points, we need to select 3 points from these 10 points. Using the combination formula:
C(10, 3) = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 10 * 3 * 4 = 120
Total number of triangles:
Since the two lines are parallel, the triangles formed using points from each line are independent of each other. Hence, the total number of triangles that can be formed using these points is the product of the number of triangles on each line:
Total number of triangles = 84 * 120 = 10080
Conclusion:
Therefore, the correct answer is 10080, not 765 as mentioned.
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Community Answer
There are two parallel lines, one of the lines has 9 points on it and ...
To make a triangle we have to take one point from one line and two point from another line
so 9C1 x 10C 2 +. 10C1 x 9C2
405 + 360 = 765
so 9C1 x 10C 2 +. 10C1 x 9C2
405 + 360 = 765
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There are two parallel lines, one of the lines has 9 points on it and the other line has 10 points on it. What is the number of triangles that can be formed using these points only (as vertices)?Correct answer is '765'. Can you explain this answer?
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