Question:

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines:

Updated On: Jul 7, 2022
  • 6
  • 9
  • 18
  • 12
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The Correct Option is C

Solution and Explanation

We know if m parallel lines are intersected by family of n parallel lines then number of parallelograms $ = {^mC_2} \times {^nC_2} = \frac{mn(m-1)(n-1)}{4}$ In given ques, m = 4, n = 3 $\therefore$ Number of parallelogram formed $ = \frac{12(3)(2)}{4} = 18 $
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Notes on Combinations

Concepts Used:

Combinations

The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.

  • It means the combination of about ‘n’ things taken ‘k’ at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.
  • For example, Imagine you go to a restaurant and order some soup.
  • Five toppings can complement the soup, namely:
    • croutons,
    • orange zest,
    • grated cheese,
    • chopped herbs,
    • fried noodles.

But you are only allowed to pick three.

  • There can be several ways in which you can enhance your soup with savory.
  • The selection of three toppings (subset) from the five toppings (larger set) is called a combination.

Use of Combinations:

It is used for a group of data (where the order of data doesn’t matter).