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 nn people in a circle is: (n1)!(n-1)! In this case, n=7n = 7, so the number of circular permutations is: (71)!=6!=720(7-1)! = 6! = 720

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:

  1. How does the formula for circular permutations differ from linear permutations?
  2. What is the reason for subtracting 1 in circular permutation problems?
  3. How can we generalize this formula for groups of different sizes?
  4. How would the answer change if the seating arrangement had restrictions, like some people must sit next to each other?
  5. 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 (n1)!(n-1)! instead of n!n!.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Permutations
Combinatorics
Circular Arrangements

Formulas

(n-1)!
6!

Theorems

Circular Permutation Theorem

Suitable Grade Level

Grades 10-12