asked 22.6k views
5 votes
Five people board an airplane that has 7 aisle seats. In how many ways can they be seated if they all select aisle​ seats?

1 Answer

4 votes

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.

answered
User Kirlich
by
8.1k points
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