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GATE 2016 EE – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

In a $2 \times 4$ rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

a grid of 2 rows and 4 columns of equal cells.
  1. 21
  2. 27
  3. 30
  4. 36

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Correct answer: (C) 30

Explanation

A rectangle in the grid is fixed by choosing 2 of the 3 horizontal lines and 2 of the 5 vertical lines. That gives $\binom{3}{2} \times \binom{5}{2} = 3 \times 10 = 30$ rectangles.