It's all in the plane

Probability Level 1

5 parallel lines in a plane are intersected by another set of 4 parallel lines.

Find the total number of parallelograms thus formed.

75 20 12 25 60

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Dinesh Nath Goswami by Dinesh Nath Goswami , 20, India

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2 solutions

Deepak Kumar
Dec 9, 2015

Chosing any 2 of the first set of parallel line and any 2 of the next set of parallel line will always form a pparallelogram. Hence 5C2*4C2=60

4 Helpful 0 Interesting 0 Brilliant 0 Confused
M S
Dec 10, 2015

Using Gauss method: n(n+1)/2 for n=a-1 where a={4,5} and multiplying both results we obtain: n1=6 n2=10 So the result is: 6 x 10 = 60

2 Helpful 0 Interesting 0 Brilliant 0 Confused

It seems you are using the sum of first n natural number formula. Can you explain why? And "Gauss method" is a bit misleading because it actually refers to Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement which is used to solve a linear system of equations.

Anupam Nayak - 5 years, 6 months ago

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