00:01
For this exercise, we are placing eight rooks randomly on a chess board, and we are asked for the probability that none of the rooks can capture any of the other rooks.
00:12
Now, rooks move only horizontally, and they can move any distance until the end of the board.
00:20
So they can move horizontally, or they can move vertically.
00:25
So that means the only way that eight randomly selected rooks cannot, such that none can capture another is such that they all occupy different rows and different columns.
00:40
For example, we could have one here, one here, one here, and so on.
00:48
As long as they are all in different rows and columns, then none of them can capture another.
00:55
So if we think of placing a rook on the first row, or let's say the first column, column a, it can take any of the eight spaces in column a.
01:10
So the number of ways to place the rooks such that they cannot capture another.
01:22
So for the first column there are eight ways...