Math Problem Statement

valuate the factorial.

8!2!

Solution

To evaluate 8!2!8! \cdot 2!, follow these steps:

Step 1: Expand the factorials

  • 8!=8×7×6×5×4×3×2×1=403208! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320
  • 2!=2×1=22! = 2 \times 1 = 2

Step 2: Multiply the results

  • 8!2!=403202=806408! \cdot 2! = 40320 \cdot 2 = 80640

Final Answer:

8!2!=806408! \cdot 2! = 80640

Do you want a breakdown of any specific steps or further clarification?

Here are 5 related questions for exploration:

  1. How do you calculate 9!3!9! \cdot 3!?
  2. What is the result of 10!/2!10! / 2!?
  3. How can factorials be simplified when dividing, e.g., 8!6!\frac{8!}{6!}?
  4. What is 5!4!5! \cdot 4! and how is it calculated?
  5. How can factorials be used in combinatorics?

Tip: When dealing with factorials, remember they grow very quickly, so simplify expressions as much as possible before calculating.

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Math Problem Analysis

Mathematical Concepts

Factorials
Arithmetic
Multiplication

Formulas

n! = n × (n-1) × ... × 2 × 1

Theorems

Factorial properties

Suitable Grade Level

Grades 6-8