the number of parallellograms that can be formed from a set of four parallei lines intersecting another set of three parallel lines is
To find the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines, you can use the following method:
Understand the pattern: Each parallelogram can be formed by selecting two vertical lines and two horizontal lines that intersect to create a closed shape.
Count the vertical lines: There are 4 vertical lines in the first set.
Count the horizontal lines: There are 3 horizontal lines in the second set.
Choose two vertical lines: You can choose 2 out of the 4 vertical lines in C(4, 2) ways, where C(n, k) represents the combination of n items taken k at a time.
Choose two horizontal lines: Similarly, you can choose 2 out of the 3 horizontal lines in C(3, 2) ways.
Calculate the total number of parallelograms: To find the total number of parallelograms, multiply the number of ways to choose vertical lines by the number of ways to choose horizontal lines:
Total parallelograms = C(4, 2) * C(3, 2)
Now, calculate:
C(4, 2) = 4! / (2!(4-2)!) = 6
C(3, 2) = 3! / (2!(3-2)!) = 3
Total parallelograms = 6 * 3 = 18
So, the number of parallelograms that can be formed is 18. The answer is indeed 18.
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