The question asks to evaluate two expressions for the given values of $n$ and $r$, where $n = 11$ and $r = 5$. Specifically, we need to compute the following:

Part (a):

$\frac{n!}{(n - r)!}$

Given:

• $n = 11$
• $r = 5$

This simplifies to: $\frac{11!}{(11 - 5)!} = \frac{11!}{6!}$

Now we calculate the factorials:

$11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6!$ The $6!$ cancels out, so we are left with: $11 \times 10 \times 9 \times 8 \times 7 = 55440$

Thus, the answer for part (a) is: $55440$

Would you like to continue to part (b)? Also, here are 5 related questions for practice:

1. What is the factorial of 6?
2. How does factorial simplify when divided by another factorial?
3. How would you compute $\frac{10!}{4!}$?
4. If $n = 12$ and $r = 6$, what is $\frac{n!}{(n - r)!}$?
5. How does the concept of permutations relate to the expression $\frac{n!}{(n - r)!}$?

Tip: Cancel out common terms in factorials to simplify large factorial expressions.