4. Three males and two females write their names on sheets of paper, and randomly arrange them in order, from left to right. What is the probability that all of the female names appear to the right of all the male names?
Solution 1: We need the first (leftmost) three names to be males and the last two names to be females. The probability that the fifth name is female is $\frac{2}{5}$. Given that the fifth name is female, the probability that the fourth name is also female is $\frac{1}{4}$. The probability that both are female is therefore $\frac{2}{5} \cdot \frac{1}{4}=\frac{1}{10}$.
Solution 2: We need the first (leftmost) three names to be males and the last two names to be females. There are $\binom{5}{2}=10$ choices for which two names are the female names, so the probability the last two names are females is $\frac{1}{10}$.