How many ways can 6 people be seated in a row? (2017)

How many ways can 6 people be seated in a row? (2017)

Step 1: Understand that we want to arrange 6 people in a row.
Step 2: Realize that the first person can be any of the 6 people.
Step 3: After the first person is seated, 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 together: 6 (for the first) × 5 (for the second) × 4 (for the third) × 3 (for the fourth) × 2 (for the fifth) × 1 (for the last).
Step 7: This multiplication is represented as 6! (6 factorial).
Step 8: Calculate 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Step 9: Conclude that there are 720 different ways to arrange 6 people in a row.

Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a set of distinct objects.