https://file.aiquickdraw.com/mathbot/file/1727406579333fi5rnbn1.jpg

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.

For the given values of n and r, evaluate (a) n! / (n - r)! and (b) n! / [r!(n - r)!] for n = 11 and r = 5.

Learn how to compute the factorial expressions for n = 11 and r = 5 using n! / (n - r)! and n! / [r!(n - r)!]. This exercise involves key concepts in permutations and combinations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation