If i have ten grains of sand on a flat, 8x8 chessboard, randomly distributed, what is the probabilty that all ten are on the same square?

Answer 1

The important thing is that the probability of a grain of sand to be one one square is equal.

Pr(on a particular square)=1/64

So if we put a grain on any one square, the next 9 have to be on that next square. The probability of that is
Pr(10 on same square)=1*(1/64)^9

which is exceedingly small.