AI-generated answer
If all five people select aisle seats, we need to determine the number of ways they can be seated in the available 7 aisle seats.
Since the order of seating does not matter, we can use the concept of combinations to solve this problem.
The number of ways to select 5 aisle seats out of the 7 available can be calculated using the combination formula:
nCr = n! / (r! * (n-r)!)
In this case, we have n = 7 (the number of available aisle seats) and r = 5 (the number of people).
Plugging these values into the formula, we get:
7C5 = 7! / (5! * (7-5)!)
Simplifying the equation further:
7C5 = 7! / (5! * 2!)
Now, let's calculate the factorial values:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
Substituting these factorial values into the equation:
7C5 = 5040 / (120 * 2) = 5040 / 240 = 21
Therefore, there are 21 different ways in which the five people can be seated if they all select aisle seats.