Problem

Two friends board an airliner just before departure time. There are only 9 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?
The 2 people can arrange ihemselves in ways.

Answer

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Answer

Final Answer: The total number of ways the two friends can arrange themselves in available seats so that at least one of them sits on the aisle is \(\boxed{38}\).

Steps

Step 1 :Consider two cases: 1. Both friends sit in aisle seats. 2. One friend sits in an aisle seat and the other does not.

Step 2 :For the first case, we have 4 aisle seats and we need to choose 2 of them for the friends. This is a combination problem, and we can use the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, and k is the number of items to choose. The number of ways for this case is \(C(4, 2) = 6\).

Step 3 :For the second case, one friend sits in an aisle seat and the other does not. We have 4 aisle seats and we need to choose 1 of them for the friend who sits in the aisle. The other friend can choose any of the remaining 8 seats (5 non-aisle seats and 3 aisle seats). This is also a combination problem. The number of ways for this case is \(C(4, 1) * C(8, 1) = 32\).

Step 4 :The total number of ways is the sum of the number of ways in these two cases, which is \(6 + 32 = 38\).

Step 5 :Final Answer: The total number of ways the two friends can arrange themselves in available seats so that at least one of them sits on the aisle is \(\boxed{38}\).

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