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.
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
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
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
Step 4 :The total number of ways is the sum of the number of ways in these two cases, which is
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