Originally Posted by
undefined Shouldn't you additionally multiply by 5! to account for the fact that the balls could be picked in 5! different orders?
If so, then the answer would agree with an alternate approach I tried:
Without loss of generality, we can suppose that the balls numbered 1 through 5 were randomly chosen, and we want the probability that exactly four match.
{1,2,3,4,x}
{1,2,3,x,5}
{1,2,x,4,5}
{1,x,3,4,5}
{x,2,3,4,5}
The above is to illustrate that there are 40*5 combinations for which exactly four match, so the probability is given by 40*5/C(45,5).