Evaluate the expression.
8 Upper P2.  8P2

The expression \(8P2\) represents the number of permutations of 8 items taken 2 at a time. The formula for permutations is:

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

In this case:
- \(n = 8\)
- \(r = 2\)

So,

\[
8P2 = \frac{8!}{(8 - 2)!} = \frac{8!}{6!}
\]

Calculating this:

\[
8! = 8 \times 7 \times 6! = 56 \times 6!
\]

Thus,

\[
\frac{8!}{6!} = 56
\]

So, \(8P2 = 56\).

Would you like a deeper explanation or have any questions?

1. What are permutations, and how do they differ from combinations?
2. How does factorial notation work in permutations?
3. Can \(8P2\) be calculated without factorials?
4. How would \(8C2\) differ from \(8P2\)?
5. How do permutations apply to real-life situations?

**Tip:** Permutations focus on arrangements where order matters.

Explore the detailed solution for evaluating the permutation expression 8P2. Understand key concepts in permutations, including the factorial formula nPr = n! / (n - r)!, and calculate how many ways to arrange 8 items in groups of 2. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation