How do you evaluate C(11, 4)?

To evaluate \[{}^{11}C_4\], we use the formula for combinations:

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

Here, \(n = 11\) and \(r = 4\). Substituting these values into the formula, we proceed as follows:

Step 1: Write the formula with the given values.
\[{}^{11}C_4 = \frac{11!}{4!(11-4)!} = \frac{11!}{4! \cdot 7!}\]

Step 2: Simplify the factorials.
The factorial \(11!\) expands as \(11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!\). Since \(7!\) is common in both the numerator and the denominator, it cancels out. This leaves:
\[\frac{11 \cdot 10 \cdot 9 \cdot 8}{4!}\]

Step 3: Calculate \(4!\).
\[4! = 4 \cdot 3 \cdot 2 \cdot 1 = 24\]

Step 4: Simplify the numerator.
\[11 \cdot 10 = 110,\]
\[110 \cdot 9 = 990,\]
\[990 \cdot 8 = 7920\]

So the numerator is \(7920\).

Step 5: Divide the numerator by \(4!\).
\[\frac{7920}{24} = 330\]

Therefore, \[{}^{11}C_4 = 330\].

Final Answer: 330