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# help

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Five different rockets, A, B, C, D and E, are to be launched from two separate launch pads labeled 1 and 2. Each pad can accommodate only one rocket at a time. The rockets can launch from either pad, in any order and at any time (sequentially or simultaneously). One example of a launch pattern is (Cl, A1D2, E1B2) where the two commas separate three different launching times. Including the example given, what is the total number of different possible launch patterns?
Sep 13, 2021

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Here is my best guess

Say they all go consecutive (no pairs)

5! ways to order them then each of those can go to pad 1 or pad 2.

So that is 5! 8 2^5 = 120*32 = 3840 ways

Now look at one pair.

There are 5C2=10 ways to choose the pair  (ty these together with a rope so now they only count as one.

There are 4! ways to line them up now.

the three singles will each have a choice of pad that is 2^3 ways

The double obviously uses both pads but can be in either order on those pads so that is 2 ways

10 * 4! * 2^3 * 2 = 10 * 24 * 16 = 3840 ways

Now look at 2 pairs

I think that there are  5C2 * 3 /2 ways to chose these = 15 ways

there are 3! ways to line them up

there are 2^3 ways to chose the pads.

15 * 6 * 8 = 720 ways

3840+ 3840 + 720 = 8400 ways

Sep 14, 2021
edited by Melody  Sep 14, 2021