Math Problem Statement
Suatu kelompok belajar yang terdiri dari 7 orang duduk melingkar. Banyak cara posisi duduk melingkar kelompok belajar tersebut adalah ....
Solution
The problem in the image is asking for the number of ways 7 people can sit in a circle, which is a question about circular permutations.
The formula for the number of ways to arrange people in a circle is: In this case, , so the number of circular permutations is:
Thus, the correct answer is 720 cara.
Would you like more details or have any questions? Here are some related questions you might find useful:
- How does the formula for circular permutations differ from linear permutations?
- What is the reason for subtracting 1 in circular permutation problems?
- How can we generalize this formula for groups of different sizes?
- How would the answer change if the seating arrangement had restrictions, like some people must sit next to each other?
- Can you apply this concept to other scenarios, such as rotating objects?
Tip: In circular permutations, the order matters but the starting point does not, which is why we use instead of .
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Math Problem Analysis
Mathematical Concepts
Permutations
Combinatorics
Circular Arrangements
Formulas
(n-1)!
6!
Theorems
Circular Permutation Theorem
Suitable Grade Level
Grades 10-12