There are 5 airplanes ready to depart. Runway A and Runway D are available. How many ways can 2 planes be assigned to the runways without using the same runway?

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High School

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Answer :

subhashreeVT subhashreeVT · Answer 1 · 2023-08-30T05:15:08-04:00

Hence, the number of ways be assigned to runways without using the same runway is [tex]240[/tex] ways.

What is the permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged.

Here given that,

Here are five airplanes ready to depart. runway [tex]A[/tex] and runway [tex]D[/tex] are available.

Number of ways to assign [tex]3[/tex] planes to that runway is

[tex]^5C_3=^5C_2=10ways[/tex]

Then for each group

Each group of three planes can be arranged in [tex]^3P_3=3!=6ways[/tex]

Each group of three planes can be arranged in [tex]^2P_2=2!=2ways[/tex]

So total number of arrangements are

[tex](2)(10)(6)(2)=240ways[/tex]

Hence, the number of ways be assigned to runways without using the same runway is [tex]240[/tex] ways.

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