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The number of straight lines obtained by joining 16 points on a plane, no twice of them being on the same line is
- a)120
- b)110
- c)210
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The number of straight lines obtained by joining 16 points on a plane,...
The no of a straight line by joining 16points on a plane ,no.twice of them being on the same
Each pair of points determine a line
16C2 = (16*15)/(1*2) = 8*15 = 120
Most Upvoted Answer
The number of straight lines obtained by joining 16 points on a plane,...
Given: 16 points on a plane
To find: Number of straight lines obtained by joining these points
Solution:
We know that a straight line is formed by joining two points.
So, we need to find the number of ways we can choose two points from 16.
This can be done using the formula for combinations:
nC2 = n(n-1)/2
where n is the total number of points
Substituting n = 16, we get:
16C2 = 16(16-1)/2
= 16*15/2
= 120
Therefore, the number of straight lines that can be obtained by joining 16 points on a plane is 120.
Hence, option A is the correct answer.
To find: Number of straight lines obtained by joining these points
Solution:
We know that a straight line is formed by joining two points.
So, we need to find the number of ways we can choose two points from 16.
This can be done using the formula for combinations:
nC2 = n(n-1)/2
where n is the total number of points
Substituting n = 16, we get:
16C2 = 16(16-1)/2
= 16*15/2
= 120
Therefore, the number of straight lines that can be obtained by joining 16 points on a plane is 120.
Hence, option A is the correct answer.
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Community Answer
The number of straight lines obtained by joining 16 points on a plane,...
To find the number of straight lines that can be formed by 16 non-collinear points in a plane, we can use the concept of combinations. Here’s the step-by-step solution:
Step 1: Understanding the Problem
We need to find the number of straight lines that can be formed by joining any two points from a set of 16 non-collinear points. Since no three points are collinear, any two points will form a unique straight line.
We need to find the number of straight lines that can be formed by joining any two points from a set of 16 non-collinear points. Since no three points are collinear, any two points will form a unique straight line.
Step 2: Using Combinations
To determine how many ways we can choose 2 points from the 16 points, we use the combination formula:
To determine how many ways we can choose 2 points from the 16 points, we use the combination formula:
In this case, n=16 (the total number of points) and r=2 (the number of points we are choosing to form a line).
Step 3: Applying the Combination Formula
Substituting the values into the formula gives us:
Substituting the values into the formula gives us:
Step 5: Calculating 2!
Calculating 2!:
Calculating 2!:
2!=2×1=2
Step 6: Final Calculation
Now substituting back into our equation:
Now substituting back into our equation:
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The number of straight lines obtained by joining 16 points on a plane, no twice of them being on the same line isa)120b)110c)210d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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