A magic bag contains some black and white balls, all of the same
size and shape.
I put my hands in the bag and simultaneously and randomly pull out
two balls. They are both the same colour and the magic bag tells me
that the chance of this occurring was exactly $0.5$.
I wonder to myself how this condition constrains the numbers of
black and white balls.
At the same time, the bag, who can read minds, says "I'll give you
a hint: it's got something nice to do with triangle
know ... ?
Probability theory has many overlaps with the study of
combinatorics. Is it fascinating how beautiful and tricky the
consequences of counting become!