11!/(11-6)!

To simplify the expression \(\frac{11!}{(11-6)!}\), we can start by calculating \(11 - 6\):

\[ 11 - 6 = 5 \]

So the expression becomes:

\[ \frac{11!}{5!} \]

Next, we can write \(11!\) in terms of \(5!\):

\[ 11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5! \]

Now substituting this into our expression:

\[ \frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5!}{5!} \]

The \(5!\) in the numerator and denominator cancel out:

\[ 11 \times 10 \times 9 \times 8 \times 7 \times 6 \]

Now, we can calculate this product step by step:

1. \(11 \times 10 = 110\)
2. \(110 \times 9 = 990\)
3. \(990 \times 8 = 7920\)
4. \(7920 \times 7 = 55440\)
5. \(55440 \times 6 = 332640\)

So, the value of \(\frac{11!}{(11-6)!}\) is:

\[ 332640 \]