Rectangles Over a Shaded Cell

Difficulty: Medium · Topics: Discrete Mathematics, Combinatorics, Counting

Bo‘yalgan katakni o‘z ichiga olgan to‘g‘ri to‘rtburchaklar

In the grid below, two cells are shaded.

graph "x":[-0.45,7.45],"y":[-0.45,5.45],"axes":false,"ink":true,"label":"A grid of 7 columns and 5 rows with two shaded cells","items":["type":"polygon","points":[[1,3],[2,3],[2,4],[1,4]],"fill":1,"ink":false,"type":"polygon","points":[[3,1],[4,1],[4,2],[3,2]],"fill":1,"ink":false,"type":"line","from":[0,0],"to":[0,5],"ink":true,"type":"line","from":[1,0],"to":[1,5],"ink":true,"type":"line","from":[2,0],"to":[2,5],"ink":true,"type":"line","from":[3,0],"to":[3,5],"ink":true,"type":"line","from":[4,0],"to":[4,5],"ink":true,"type":"line","from":[5,0],"to":[5,5],"ink":true,"type":"line","from":[6,0],"to":[6,5],"ink":true,"type":"line","from":[7,0],"to":[7,5],"ink":true,"type":"line","from":[0,0],"to":[7,0],"ink":true,"type":"line","from":[0,1],"to":[7,1],"ink":true,"type":"line","from":[0,2],"to":[7,2],"ink":true,"type":"line","from":[0,3],"to":[7,3],"ink":true,"type":"line","from":[0,4],"to":[7,4],"ink":true,"type":"line","from":[0,5],"to":[7,5],"ink":true]

How many rectangles formed by the grid lines contain at least one shaded cell?