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A group of k Vikings independently set out to make a new home. Each Viking has...

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Advance Math

A group of k Vikings independently set out to make a new home.Each Viking has a copy of the same map, showing n islands. EachViking decides to set sail for some random island. If two or moreVikings land on the same island, they have a battle. (No matter howmany Vikings land on that island, it counts as one battle.)

(a) How many battles do we expect will occur? (Hint: Fix asingle island, what is the probability of no viking ever landingthere? What about exactly one viking reaching this island? What isthe relationship of these events and there being a fight in theisland?)

(b) You should have obtained a closed formula that depends on nand k. For both formulas, consider the cases in which there is onlyone island on the map. Do your solutions confirm the intuitiveanswer for this case? What if there’s only one Viking? What answersdo you get for 400 Vikings and 100 islands?

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