If `""^(n)C_(a)= ""^(n)C_(b)`' then find n.

Answer

To solve the problem where \( \binom{n}{a} = \binom{n}{b} \), we will use the properties of combinations.

### Step-by-step Solution:

1. **Understanding the Property of Combinations**:
We know that \( \binom{n}{r} = \binom{n}{n-r} \). This means that the number of ways to choose \( r \) items from \( n \) is the same as choosing \( n-r \) items from \( n \).

2. **Setting Up the Equation**:
Given that \( \binom{n}{a} = \binom{n}{b} \), we can apply the property mentioned above. This implies:
\[ \binom{n}{a} = \binom{n}{n-b} \]

3. **Equating the Indices**:
From the equality \( \binom{n}{a} = \binom{n}{n-b} \), we can conclude that:
\[ a = n - b \quad \text{or} \quad b = n - a \]

4. **Finding the Value of \( n \)**:
Rearranging the equation \( a + b = n \), we find:
\[ n = a + b \]

5. **Conclusion**:
Therefore, the value of \( n \) is given by:
\[ n = a + b \]

### Final Answer:
The value of \( n \) is \( a + b \).