For expansion of `(1 + x)^(n)` , coefficient of 5th term is ___

Answer

To find the coefficient of the 5th term in the expansion of \((1 + x)^n\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the General Term**:
The general term \(T_{r+1}\) in the expansion of \((a + b)^n\) is given by:
\[ T_{r+1} = \binom{n}{r} a^{n-r} b^r \]
For our case, \(a = 1\) and \(b = x\), so the general term becomes:
\[ T_{r+1} = \binom{n}{r} (1)^{n-r} (x)^r = \binom{n}{r} x^r \]

2. **Determine the 5th Term**:
The 5th term corresponds to \(r = 4\) (since \(r\) starts from 0). Therefore, we need to find \(T_5\):
\[ T_5 = \binom{n}{4} x^4 \]

3. **Extract the Coefficient**:
The coefficient of the 5th term is simply the binomial coefficient \(\binom{n}{4}\):
\[ \text{Coefficient of the 5th term} = \binom{n}{4} \]

### Final Answer:
The coefficient of the 5th term in the expansion of \((1 + x)^n\) is \(\binom{n}{4}\).