Question 751345: There are 5 airplanes ready to depart. Runway A and runway D are available. How many ways can 2 planes be assigned to runways without using the same runway?
Could you please tell me the answer, and teach me which is N and which is R from the permutation formula, it is a permutation right? Thank you so much for taking the time to answer my question.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are 5 airplanes ready to depart. Runway A and runway D are available. How many ways can 2 planes be assigned to runways without using the same runway?
Could you please tell me the answer, and teach me which is N and which is R from the permutation formula, it is a permutation right? Thank you so much for taking the time to answer my question.
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Pick a runway: 2 ways
# of ways to assign 3 planes to that runway: 5C3 = 5C2 = 10 ways
Note: Every assignment of 3 to that runway assigns 2 planes to the other.
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Each group of 3 planes can be arranged in 3P3 = 3! = 6 ways
Each group of 2 planes can be arranged in 2P2 = 2! = 2 ways
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Total # of arrangements: 2*10*6*2 = 240 ways
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Cheers,
Stan H.
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