Question

an movie theatre has a row of 6 seats for 6 friends to sit in. the friends sit in the row in the order that they randomly arrive. how many different seating arrangements are possible?

Answer 1

There are 720 different seating arrangements possible for 6 friends sitting in a row of 6 seats in a movie theatre. This is found using permutations, where the number of options for each seat is multiplied together.

Step-by-step explanation:

To determine the number of different seating arrangements possible for 6 friends in a movie theatre with 6 seats, we use the concept of permutations, where order matters. The first friend has 6 choices of seats, the second will have 5 remaining choices, and so on, down to the last friend having only 1 choice left. Therefore, the total number of possible seating arrangements is calculated by multiplying these choices together, which means 6 x 5 x 4 x 3 x 2 x 1.

The calculation is:

1. 6 choices for the first seat
2. 5 choices for the second seat
3. 4 choices for the third seat
4. 3 choices for the fourth seat
5. 2 choices for the fifth seat
6. 1 choice for the sixth seat

By multiplying these numbers (6 factorial), we find that there are 720 different seating arrangements possible.