Question: In how many ways can 4 people be seated at a round table?
Options:
24
12
6
4
Correct Answer: 12
Solution:
The number of arrangements of 4 people at a round table is (4-1)! = 6.
In how many ways can 4 people be seated at a round table?
Practice Questions
Q1
In how many ways can 4 people be seated at a round table?
24
12
6
4
Questions & Step-by-Step Solutions
In how many ways can 4 people be seated at a round table?
Correct Answer: 6
Step 1: Understand that seating people at a round table is different from a straight line because the arrangement is circular.
Step 2: Realize that when arranging people in a circle, one person's position can be fixed to avoid counting the same arrangement multiple times.
Step 3: Fix one person in a seat. This means we only need to arrange the remaining 3 people.
Step 4: Calculate the number of ways to arrange the remaining 3 people. This is done by finding the factorial of the number of people left, which is 3.
Step 5: Calculate 3! (3 factorial), which is 3 x 2 x 1 = 6.
Step 6: Conclude that the total number of ways to seat 4 people at a round table is 6.
Circular Permutations – In circular arrangements, one position is fixed to account for rotations, leading to (n-1)! arrangements for n people.
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