Math Problem Statement
Hitunglah nilai dari: a. 3!, b. 4! - 2!, c. 6! x 2, d. 8! / [5!(8-5)!], e. 10! / 9! x 2!
Solution
The image contains a mathematical problem asking to compute several factorial expressions. Let me solve each part for you.
Problem Breakdown
The problem asks to compute the values for the following expressions:
a.
b.
c.
d.
e.
Let's calculate each part one by one.
Solutions:
a.
b.
So,
c.
d.
The expression can be simplified as:
Now, compute the factorials:
So:
e.
Since ,
Final Answers:
- a. 6
- b. 22
- c. 1440
- d. 56
- e. 20
Would you like more details on any of these calculations or have any questions?
Related Questions:
- What are factorials, and why are they used in mathematics?
- How do combinations and permutations differ, and where do factorials come into play?
- What is the relationship between factorials and exponential functions?
- How can factorial calculations be optimized for larger numbers?
- What are some real-world applications of factorials in probability and statistics?
Tip: Understanding the properties of factorials can help simplify complex combinatorial problems.
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Math Problem Analysis
Mathematical Concepts
Factorial
Basic Arithmetic
Formulas
n! = n × (n-1) × ... × 1
(n! / r!(n-r)!) for combinations
Theorems
Combinatorial Theorem
Basic Properties of Factorials
Suitable Grade Level
Grades 9-10