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?
  1. 720
  2. 600
  3. 480
  4. 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.
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