If `""^(12)C_(5) + ^(12)C_(6) = ^(x)C_(6)` then x = _________

Answer

To solve the equation \( \binom{12}{5} + \binom{12}{6} = \binom{x}{6} \), we can use a property of combinations.

### Step-by-Step Solution:

1. **Identify the Combination Property**: We know that the combination property states:
\[ \binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} \]
In our case, we can identify \( n = 12 \), \( r = 5 \), and \( r + 1 = 6 \).

2. **Apply the Property**: According to the property:
\[ \binom{12}{5} + \binom{12}{6} = \binom{12 + 1}{6} = \binom{13}{6} \]

3. **Set the Equation**: Now we can rewrite the original equation:
\[ \binom{12}{5} + \binom{12}{6} = \binom{13}{6} \]
Therefore, we have:
\[ \binom{x}{6} = \binom{13}{6} \]

4. **Compare the Two Sides**: Since the combinations are equal, we can conclude that:
\[ x = 13 \]

### Final Answer:
Thus, the value of \( x \) is \( 13 \).

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