# question on probability theory

An urn contains five red balls and three yellow balls. Four balls are drawn from the urn at random, without replacement. What is probability that the first two balls are red and the second two balls are yellow?

$$\frac{5(redballs)}{8(allballs)}\times \frac{4(redballs)}{7(allballs)}\times \frac{3(yellowballs)}{6(allballs)} \times \frac{2(yellowballs)}{5(allballs)} = 0.0714$$
$$P(R_1\cap R_2\cap Y_3\cap Y_4)=P(R_1)P(R_2\mid R_1)P(Y_3\mid R_1\cap R_2)P(Y_4\mid R_1\cap R_2\cap Y_3)=\frac58\frac47\frac36\frac25$$