randomly picking balls
There are m red balls labeled as r1,r2,.,rm and n blue balls labeled as b1,b2,.,bn in a bag. We draw them out of the bag without replacement until the last ball is picked out. Suppose at each drawing, all balls remaining in the bag always have equal probabilities of being picked out. What is the probability that both the red balls and the blue balls are drawn out in the numerical order (that is, ri is the i-th red ball to be picked out and bi is the i-th blue ball to be picked out) ?