Grid based problem Concept
Example:- Find the number of rectangles in 10×12 grid.
Solution:-
¹⁰⁺¹C₂ × ¹²⁺¹C₂
= ¹¹C₂ × ¹³C₂
= 55 × 78
= 4290 Answer
Example:- Find the number of squares in 10×12 grid.
Solution:-
10×12 = 120
9×11 = 99
8×10 = 80
7×9 = 63
6×8 = 48
5×7 = 35
4×6 = 24
3×5 = 15
2×4 = 8
1×3 = 3
________
Total = 495
________
Hence total number of squares = 495 Answer