Trillian's mice III
If four mice are chosen at random (without replacement), the probability that two are white is equal to the probability that none are white.
Given further that Trillian has more mice than toes (of which she has the usual ten), what's the least number of mice she could possibly have?
NB. This is the final—and hardest—problem in a series of three. You are encouraged to solve the previous problems first.