4. In the box, there are 3 white cups, 3 red cups, and 2 black cups. Sonya took out 5 cups at random. What is the probability that she took out 2 white, 2 red, and 1 black cup? (Round the answer to the nearest hundredth).
Solution:

Let white cups be denoted as W, red cups as R, and black cups as B.

1) The probability of drawing 2 white, then 2 red, and then 1 black cup, in the order WWR RB: $\frac{3}{8} \cdot \frac{2}{7} \cdot \frac{3}{6} \cdot \frac{2}{5} \cdot \frac{2}{4}=\frac{3}{280}$

2) The number of ways to rearrange the letters in the sequence WWR RB is:

$$
\frac{5!}{2!\cdot 2!}=30
$$

3) $\frac{30 \cdot 3}{280}=\frac{9}{28}$

Answer: 0.32