probability that 5 square lie along a diagonal line If $5$ squares are chosen at random from a chess board, what is the probability that they lie on a diagonal line?
HINT: 


There are $64$ squares altogether; how many ways are there to choose $5$ of them?
There are $15$ diagonals in each direction, but only $7$ of them are long enough to contain $5$ squares. Specifically, in each direction there are two diagonals of length $5$, two of length $6$, two of length $7$, and one of length $8$. How many $5$-element subsets are there of each of these diagonals? 


The total in (2) is the number of sets of $5$ squares that lie on a diagonal. The total in (1) is the total number of sets of $5$ squares. Combine these two numbers to get the desired probability.
There is $16$ possible arrangements of $5$ squares so that they are on the diagonal lines and $64*63*62*61*60$ possible ways to put squares on the chessboard so the probability is $16\over(64*63*62*61*60)$