Evaluate
` C(8,5)`

Answer

To evaluate \( C(8, 5) \), we will use the formula for combinations, which is given by:

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

### Step 1: Identify the values of \( n \) and \( r \)
In this case, we have:
- \( n = 8 \)
- \( r = 5 \)

### Step 2: Substitute the values into the combination formula
Now, substituting the values into the formula:

\[ C(8, 5) = \frac{8!}{5!(8 - 5)!} \]

### Step 3: Simplify the expression
Calculate \( 8 - 5 \):

\[ 8 - 5 = 3 \]

So, we can rewrite the expression as:

\[ C(8, 5) = \frac{8!}{5! \cdot 3!} \]

### Step 4: Expand the factorials
Now, we can expand the factorials:

\[ 8! = 8 \times 7 \times 6 \times 5! \]

Thus, substituting this back into our equation gives us:

\[ C(8, 5) = \frac{8 \times 7 \times 6 \times 5!}{5! \cdot 3!} \]

### Step 5: Cancel out \( 5! \)
The \( 5! \) in the numerator and denominator cancels out:

\[ C(8, 5) = \frac{8 \times 7 \times 6}{3!} \]

### Step 6: Calculate \( 3! \)
Now, calculate \( 3! \):

\[ 3! = 3 \times 2 \times 1 = 6 \]

### Step 7: Substitute \( 3! \) back into the equation
Now substitute \( 3! \) back into the equation:

\[ C(8, 5) = \frac{8 \times 7 \times 6}{6} \]

### Step 8: Simplify the expression
Now, we can simplify:

\[ C(8, 5) = 8 \times 7 = 56 \]

### Final Answer
Thus, the value of \( C(8, 5) \) is:

\[ \boxed{56} \]