From a group of 2 boys and 3 girls, two children are selected at random. Describe the events:
(i) A: both selected children are girls
(ii) B: the selected group consists o one boy and one girl
(iii)C: atleast one boy is selected.

Answer

To solve the problem, we need to describe the events based on the selection of children from a group of 2 boys and 3 girls. Let's denote the boys as B1, B2 and the girls as G1, G2, G3.

### Step-by-Step Solution:

1. **Identify the total number of children**:
- There are 2 boys (B1, B2) and 3 girls (G1, G2, G3).
- Total children = 2 boys + 3 girls = 5 children.

2. **Determine the total number of ways to select 2 children from 5**:
- The number of ways to choose 2 children from 5 can be calculated using the combination formula \( C(n, r) = \frac{n!}{r!(n-r)!} \).
- Here, \( n = 5 \) and \( r = 2 \):
\[ C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

3. **Event A: Both selected children are girls**:
- The possible combinations of selecting 2 girls from 3 are:
- G1, G2
- G1, G3
- G2, G3
- Therefore, the outcomes for event A are: {G1, G2}, {G1, G3}, {G2, G3}.
- Total outcomes for event A = 3.

4. **Event B: The selected group consists of one boy and one girl**:
- The possible combinations are:
- B1, G1
- B1, G2
- B1, G3
- B2, G1
- B2, G2
- B2, G3
- Therefore, the outcomes for event B are: {B1, G1}, {B1, G2}, {B1, G3}, {B2, G1}, {B2, G2}, {B2, G3}.
- Total outcomes for event B = 6.

5. **Event C: At least one boy is selected**:
- The combinations that include at least one boy are:
- B1, G1
- B1, G2
- B1, G3
- B2, G1
- B2, G2
- B2, G3
- B1, B2 (both boys)
- Therefore, the outcomes for event C are: {B1, G1}, {B1, G2}, {B1, G3}, {B2, G1}, {B2, G2}, {B2, G3}, {B1, B2}.
- Total outcomes for event C = 7.

### Summary of Events:
- **Event A**: {G1, G2}, {G1, G3}, {G2, G3} (3 outcomes)
- **Event B**: {B1, G1}, {B1, G2}, {B1, G3}, {B2, G1}, {B2, G2}, {B2, G3} (6 outcomes)
- **Event C**: {B1, G1}, {B1, G2}, {B1, G3}, {B2, G1}, {B2, G2}, {B2, G3}, {B1, B2} (7 outcomes)