8 Dec
2003
8 Dec
'03
9:44 p.m.
My apologies; I sent the previous message prematurely. I was saying: there are n(n-1) ways of picking two balls to be numbered 1 and 2. Of these ways, (n-k)(n-k-1) have neither ball red. So the desired probability is {n(n-1)-(n-k)(n-k-1)}/n(n-1). Simplifying, this is k(2n-k-1)/n(n-1). For the given example, n=20 and k=7, for which the formula gives 56/95. -ACW