You and 5 friends go to a concert. In how many different orders can you sit in the assigned seats?
you and friends = 6 people
6! permutations
To determine the number of different orders in which you and your 5 friends can sit in the assigned seats at the concert, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, the objects are the 6 people, including yourself, and the order matters because each seat is assigned.
The formula for calculating permutations is:
P(n, r) = n! / (n - r)!
In this equation:
- n is the total number of objects (in this case, the 6 people)
- r is the number of objects arranged at a time (in this case, also 6, since all 6 people need to be seated)
Using the formula, we can calculate the number of different orders:
P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
= 6! / 1
= 6 x 5 x 4 x 3 x 2 x 1 / 1
= 720
Therefore, there are 720 different orders in which you and your 5 friends can sit in the assigned seats at the concert.