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The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
- a)6
- b)18
- c)12
- d)9
Correct answer is option 'B'. Can you explain this answer?
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Solution:
The number of parallelograms that can be formed by joining the vertices of a set of parallel lines intersecting another set of parallel lines is given by the formula:
Number of parallelograms = (number of ways of choosing 2 horizontal lines) x (number of ways of choosing 2 vertical lines)
= (4C2) x (3C2)
= 6 x 3
= 18
Therefore, option B is the correct answer.
The number of parallelograms that can be formed by joining the vertices of a set of parallel lines intersecting another set of parallel lines is given by the formula:
Number of parallelograms = (number of ways of choosing 2 horizontal lines) x (number of ways of choosing 2 vertical lines)
= (4C2) x (3C2)
= 6 x 3
= 18
Therefore, option B is the correct answer.
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The number of parallelograms that can be formed from a set of four par...
To form a parallelogram, we need to select two lines from one set of parallel lines and two lines from the other set. The intersection of these lines will give the four corners of the parallelogram.
Step 1: Number of ways to choose 2 lines from 4 parallel lines
This can be calculated using the combination formula ιnr, where n is the total number of lines and r is the number of lines we want to choose. So, the number of ways to choose 2 lines from 4 is:
This can be calculated using the combination formula ιnr, where n is the total number of lines and r is the number of lines we want to choose. So, the number of ways to choose 2 lines from 4 is:
ι42 = (4 × 3) / (2 × 1) = 6
Step 2: Number of ways to choose 2 lines from 3 parallel lines
Similarly, the number of ways to choose 2 lines from 3 is:
Similarly, the number of ways to choose 2 lines from 3 is:
ι32 = (3 × 2) / (2 × 1) = 3
Step 3: Total number of parallelograms
Now, to form a parallelogram, we multiply the number of ways to choose 2 lines from each set:
Now, to form a parallelogram, we multiply the number of ways to choose 2 lines from each set:
Total number of parallelograms = ι42 × ι32 = 6 × 3 = 18
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The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines isa)6b)18c)12d)9Correct answer is option 'B'. Can you explain this answer?
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