Question: In how many ways can 6 people be seated in a row?
Options:
720
600
480
360
Correct Answer: 720
Solution:
The number of arrangements of 6 people is 6! = 720.
In how many ways can 6 people be seated in a row?
Practice Questions
Q1
In how many ways can 6 people be seated in a row?
720
600
480
360
Questions & Step-by-Step Solutions
In how many ways can 6 people be seated in a row?
Step 1: Understand that we have 6 people who need to be seated in a row.
Step 2: Realize that the first person can be any of the 6 people.
Step 3: After seating the first person, there are 5 people left to choose from for the second seat.
Step 4: For the third seat, there are 4 people left to choose from.
Step 5: Continue this process: for the fourth seat, there are 3 people left; for the fifth seat, there are 2 people left; and for the last seat, there is only 1 person left.
Step 6: Multiply the number of choices for each seat together: 6 × 5 × 4 × 3 × 2 × 1.
Step 7: This multiplication is represented by 6! (6 factorial), which equals 720.
Step 8: Therefore, the total number of ways to seat 6 people in a row is 720.
Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a set of distinct objects.
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