In how many ways 2 persons can be selected from 4 persons?

Answer

To solve the problem of selecting 2 persons from a group of 4 persons, we can use the concept of combinations. The formula for combinations is given by:

\[ nCr = \frac{n!}{r!(n-r)!} \]

Where:
- \( n \) is the total number of items (in this case, 4 persons),
- \( r \) is the number of items to choose (in this case, 2 persons),
- \( ! \) denotes factorial, which is the product of all positive integers up to that number.

### Step-by-Step Solution:

1. **Identify n and r**:
- Here, \( n = 4 \) (the total number of persons),
- \( r = 2 \) (the number of persons to select).

2. **Apply the combinations formula**:
- We need to calculate \( 4C2 \):
\[ 4C2 = \frac{4!}{2!(4-2)!} \]

3. **Calculate the factorials**:
- First, calculate \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]
- Next, calculate \( 2! \):
\[ 2! = 2 \times 1 = 2 \]
- Now, calculate \( (4-2)! = 2! \):
\[ 2! = 2 \times 1 = 2 \]

4. **Substitute the values into the formula**:
\[ 4C2 = \frac{24}{2 \times 2} = \frac{24}{4} = 6 \]

5. **Conclusion**:
- Therefore, the total number of ways to select 2 persons from 4 persons is **6**.