Consider a regular 8x8 chessboard. Precisely four distinct squares are chosen randomly on the chessboard.
Determine the probability that they lie in the same diagonal.
There are four each of length4, 5, 6, and 7 diagonals, and two length 8.
In each, the number of ways is C(n,4).
So the number of ways is 4*(C(4,4) + C(5,4) + C(6,4) + C(7,4)) + 2*C(8,4) = 4 * (1+5+15+35)+2*70 = 364.
There are C(64,4) ways of getting four random places.
So that's a probability of 364/635376 = 182/317688 ~= .000572889123920324.

Posted by Charlie
on 20141104 08:33:07 