You and five friends- a total of six parties- plan to meet once per month to have dinner together,with one of you choosing the restaurant each month. Rather than scheduling the entire year in advance, you decide to make it interesting: each month a single six-sided die will be rolled to determine which of you gets to choose the restaurant that month. How likely is it that everyone will have a chance to eat at their own favorite restaurant? That is, what is the probability that over the next 12 months, each of you will have had at least one opportunity to choose where to eat?

Use inclusion-exclusion to derive a formula and compute the exact desired probability .(Note: in practical applications, in many cases, this step is impossible. In other cases,observing empirical behavior like above can provide insight leading to an exact solution.)

When severe drought much Mediterranean Agean->Nile, central gov collapsed->attacks outside + powerful vassals threw off allegiance -Uluburun and Maritime Trade: diplomatic/military activity->control gold/copper/pottery trade e.Mediterranean/Mycenaean traders off s.Turkish coast, Uluburun-ship @ Cemal Pulak s.Turkey, shipwrecked 1310BC, carried 350+ copper ingots (60 pounds each), load 10 tons (enough 2 equip small army w/ weapons/armor), a ton resin (2-handled jars) 4 people in Syria used as incense 4 Egyptian rituals, dozens blue glass disks, ingots sent Egypt fm Tyre, hardwood, Baltic amber, tortoise shells, elephant tusks, hippopotamus teeth, ostrich eggs, jars olives, Canaanite/Mycenaean pottery, fm Africa, Egypt, e. Mediterranean coast, Greek mainland-Aegean, Cyprus, Sardinia, reflection-interantional nature e.Mediterranean trade in 2 nd millennium BC-Hittites @ height power -Iron Technology: maritime trade-role diffusion irons tools/weapons e.Mediterranean, iron thought have been