Question: How many ways can 4 people be seated at a round table?
Options:
6
12
24
30
Correct Answer: 6
Solution:
The number of arrangements of 4 people at a round table is (4-1)! = 3! = 6.
How many ways can 4 people be seated at a round table?
Practice Questions
Q1
How many ways can 4 people be seated at a round table?
6
12
24
30
Questions & Step-by-Step Solutions
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 rotations of the same arrangement are considered the same.
Step 2: To find the number of unique arrangements, we can fix one person in place to eliminate the effect of rotation.
Step 3: After fixing one person, we only need to arrange the remaining 3 people around the table.
Step 4: The number of ways to arrange 3 people is calculated as 3! (3 factorial).
Step 5: Calculate 3! which is 3 x 2 x 1 = 6.
Step 6: Therefore, 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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