Find the value of :
` ""^(50)C_(47)`

Answer

To find the value of \( \binom{50}{47} \), we will use the formula for combinations, which is given by:

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

### Step-by-Step Solution:

1. **Identify the values of n and r**:
Here, \( n = 50 \) and \( r = 47 \).

2. **Apply the combination formula**:
Using the formula, we have:
\[ \binom{50}{47} = \frac{50!}{47!(50-47)!} = \frac{50!}{47! \cdot 3!} \]

3. **Simplify the factorials**:
We can express \( 50! \) as:
\[ 50! = 50 \times 49 \times 48 \times 47! \]
Therefore, substituting this back into our equation gives:
\[ \binom{50}{47} = \frac{50 \times 49 \times 48 \times 47!}{47! \cdot 3!} \]

4. **Cancel out the \( 47! \)**:
The \( 47! \) in the numerator and denominator cancels out:
\[ \binom{50}{47} = \frac{50 \times 49 \times 48}{3!} \]

5. **Calculate \( 3! \)**:
We know that:
\[ 3! = 3 \times 2 \times 1 = 6 \]

6. **Substitute \( 3! \) back into the equation**:
Thus, we have:
\[ \binom{50}{47} = \frac{50 \times 49 \times 48}{6} \]

7. **Perform the multiplication**:
First, calculate \( 50 \times 49 \times 48 \):
\[ 50 \times 49 = 2450 \]
\[ 2450 \times 48 = 117600 \]

8. **Divide by 6**:
Now, divide \( 117600 \) by \( 6 \):
\[ \frac{117600}{6} = 19600 \]

### Final Answer:
Thus, the value of \( \binom{50}{47} \) is \( 19600 \).