What is the probability that two 1 by 1 squares selected randomly from

Hello, could you please explain this part:
Also. we have a total of 9*9 = 81 corner, out of which only some satisfy the condition. We can find the required number of squares in two ways:
1. Count individually the corners that are inside the chess board - ones which are shared by 4 squares i.e. 7*7 = 49
2. Subtract the outside corners that have only either 2 squares sharing one or the 4 corners of the big chess board square. 9*9 - 4*1 - 7*4 = 49

why do we have a total of 9x9 corner ?

sthahvi
First draw a chessboard to understand.
Assuming that you know what i did, I'll explain only 9*9 corner part.

Like an 8-lane highway has 9 lines - 2 are extreme ones and 7 are inside - OR like an athlete track has 8 lanes with 9 lines, a chess board has 8-rows and 8-columns that criss-cross each other leaving 64 squares.
You can either count the corners manually and find that there are 9 horizontal(row) lines and 9 vertical(column) lines.

OR

Slightly longer version.
We have 64 squares with each having 4 corners i.e. 64*4 corners in total. But there are some squares that share a corners, thus corners are counted twice or thrice. Ways in which squares share corners are:
1. Corners shared by 0 squares - 1st and the 64th(unless you count them in a way that the two share a corner/s ) e.g. the diagonally opposite squares far separated by each other. Here no corner is counted twice or thrice.
2. Corners shared by 2 squares - ones that lie on the outside line(4 edges of the big chess-board square). There is a double counting here.
3. Corners shared by 4 squares - an extension of point 2(by this time you will know which ones). Here again there is double counting which happens as in where a corner is shared by four squares, eventually counting a corner four times.

So, we have to subtract the double counting and quadruple counting by one time and three times respectively.
Total corners = 64*4 - 1*7*4 - 3*7*7 = 81

Also, in my original post '1'(highlighted) refers to number of corners and it has got no significance in the term '4*1'. It should have been just '4'.

Hope my original post and this one make sense in totality now.

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