19. There are 8 people in a room: 3 of them have red hair, 2 have blonde hair, and the rest have dark hair. Two people are randomly selected to leave the room, one after another, and they do not re-enter the room. A) What is the probability ff a person with dark hair leaving the room first? B) What is the probability of a person with red hair leaving the room, followed by a person with blonde hair? C) What is the probability of two people with dark hair color leaving the room?

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### Known Conditions:
- Total people in the room: 8
- People with red hair: 3
- People with blonde hair: 2
- People with dark hair: $$8 - 3 - 2 = 3$$

### A) Probability of a person with dark hair leaving the room first

To find the probability of selecting a person with dark hair first, we can use the formula for probability:

$$
P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}
$$

1. **Number of favorable outcomes** (people with dark hair): 3
2. **Total outcomes** (total people): 8

Thus, the probability $$P(D_1)$$ of a person with dark hair leaving first is:

$$
P(D_1) = \frac{3}{8}
$$

### B) Probability of a person with red hair leaving the room, followed by a person with blonde hair

To find this probability, we need to consider two events:
1. The first person selected is from the red-haired group.
2. The second person selected is from the blonde-haired group.

1. **Probability of selecting a red-haired person first**:
   - Number of red-haired people: 3
   - Total people: 8

$$
   P(R_1) = \frac{3}{8}
   $$

2. **Probability of selecting a blonde-haired person second** (after one red-haired person has left):
   - Remaining people: 7 (since one red-haired person has left)
   - Number of blonde-haired people: 2

$$
   P(B_2 | R_1) = \frac{2}{7}
   $$

Now, we multiply these probabilities to find the combined probability:

$$
P(R_1 \text{ and } B_2) = P(R_1) \times P(B_2 | R_1) = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}
$$

### C) Probability of two people with dark hair leaving the room

To find the probability of selecting two people with dark hair, we consider the following:

1. **Probability of selecting the first dark-haired person**:
   - Number of dark-haired people: 3
   - Total people: 8

$$
   P(D_1) = \frac{3}{8}
   $$

2. **Probability of selecting the second dark-haired person** (after one dark-haired person has left):
   - Remaining people: 7
   - Remaining dark-haired people: 2

$$
   P(D_2 | D_1) = \frac{2}{7}
   $$

Now, we multiply these probabilities to find the combined probability:

$$
P(D_1 \text{ and } D_2) = P(D_1) \times P(D_2 | D_1) = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}
$$

### Summary of Results:
- A) Probability of a person with dark hair leaving first: $$\frac{3}{8}$$
- B) Probability of a person with red hair leaving, followed by a person with blonde hair: $$\frac{3}{28}$$
- C) Probability of two people with dark hair leaving: $$\frac{3}{28}$$
A) The probability of a person with dark hair leaving first is 3/8. B) The probability of a person with red hair leaving first, followed by a person with blonde hair is 3/28. C) The probability of two people with dark hair leaving is 3/28.

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