Evaluate
` ""^(11)C_(2)`.

Answer

To evaluate \( \binom{11}{2} \), we will use the formula for combinations, which is given by:

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

In this case, \( n = 11 \) and \( r = 2 \).

### Step 1: Substitute the values into the formula
We substitute \( n \) and \( r \) into the formula:

\[ \binom{11}{2} = \frac{11!}{2!(11-2)!} \]

### Step 2: Simplify the expression
Now, simplify \( 11 - 2 \):

\[ \binom{11}{2} = \frac{11!}{2! \cdot 9!} \]

### Step 3: Expand the factorials
Next, we expand \( 11! \):

\[ 11! = 11 \times 10 \times 9! \]

So, we can rewrite our expression:

\[ \binom{11}{2} = \frac{11 \times 10 \times 9!}{2! \cdot 9!} \]

### Step 4: Cancel out the common terms
The \( 9! \) in the numerator and denominator cancels out:

\[ \binom{11}{2} = \frac{11 \times 10}{2!} \]

### Step 5: Calculate \( 2! \)
Now, calculate \( 2! \):

\[ 2! = 2 \times 1 = 2 \]

### Step 6: Substitute and simplify
Substituting \( 2! \) back into the equation gives us:

\[ \binom{11}{2} = \frac{11 \times 10}{2} \]

### Step 7: Perform the multiplication and division
Now, calculate \( 11 \times 10 \):

\[ 11 \times 10 = 110 \]

Now divide by \( 2 \):

\[ \frac{110}{2} = 55 \]

### Final Answer
Thus, the value of \( \binom{11}{2} \) is:

\[ \boxed{55} \]