In a 2 x 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? [2 rows, 4 columns of cells] A. 21 B. 27 C. 30 D. 36

GATE 2016 · General Aptitude · Combinatorics · medium

Answer: 30 rectangles (option C)

1. Count horizontal-line pairs: Rows = 2, so horizontal lines = 2+1 = 3. Choose 2: C(3,2) = 3!/(2!*1!) = 3.
2. Count vertical-line pairs: Columns = 4, so vertical lines = 4+1 = 5. Choose 2: C(5,2) = 5!/(2!*3!) = 10.
3. Apply product rule: Total rectangles = C(3,2) x C(5,2) = 3 x 10 = 30.