A committee of 2 boys is to be selected from 4 boys. In how many ways can this be done ?

Answer

To solve the problem of selecting a committee of 2 boys from a group of 4 boys, we can use the concept of combinations. Here's the step-by-step solution:

### Step 1: Identify the values of N and R
- **N** is the total number of boys, which is 4.
- **R** is the number of boys to be selected, which is 2.

### Step 2: Use the combination formula
The formula for combinations is given by:
\[ ^nC_r = \frac{n!}{(n - r)! \cdot r!} \]
In our case, we need to calculate \( ^4C_2 \).

### Step 3: Substitute the values into the formula
Substituting \( N = 4 \) and \( R = 2 \) into the formula:
\[ ^4C_2 = \frac{4!}{(4 - 2)! \cdot 2!} \]

### Step 4: Calculate the factorials
Now, we need to calculate the factorials:
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)
- \( (4 - 2)! = 2! = 2 \times 1 = 2 \)
- \( 2! = 2 \times 1 = 2 \)

### Step 5: Substitute the factorial values back into the formula
Now we can substitute these values back into our combination formula:
\[ ^4C_2 = \frac{24}{2 \cdot 2} = \frac{24}{4} \]

### Step 6: Simplify the expression
Now, simplify the expression:
\[ ^4C_2 = 6 \]

### Conclusion
Thus, the number of ways to select a committee of 2 boys from 4 boys is **6**.

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