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In how many ways can 6 people be seated in a round table?
In how many ways can 6 people be seated in a round table?
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Practice Questions
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Q1
In how many ways can 6 people be seated in a round table?
720
120
60
30
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The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 6 people be seated in a round table?
Solution:
The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.
Steps: 6
Show Steps
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 by finding the factorial of 5, which is written as 5!.
Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 6: Conclude that the total number of ways to arrange 6 people at a round table is 120.
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