How many different ways can 6 people be seated at a round table?
Practice Questions
1 question
Q1
How many different ways can 6 people be seated at a round table?
720
120
600
480
The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.
Questions & Step-by-step Solutions
1 item
Q
Q: How many different ways can 6 people be seated at a round table?
Solution: The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.
Steps: 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 you only need to arrange the remaining 5 people.
Step 4: Calculate the number of ways to arrange the remaining 5 people. This is done using the factorial of the number of people, which is 5! (5 factorial).
Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 6: Conclude that there are 120 different ways to seat 6 people at a round table.
