Question:

The number of rectangles which we can form on a chess board is

Updated On: Jul 7, 2022
  • $81$
  • $1296$
  • $648$
  • $324$
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The Correct Option is B

Solution and Explanation

There ate 9 horizontal and 9 vertical lines on a chess board. To from a rectangle we require two horizontal and two vertical lines. Thus the no. of rectangles on the chess board $=\,^{9}C_{2} \times \,^{9}C_{2}=36 \times 36$ $=1296$.
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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).