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A survey was conducted of 800 people who drink coffee in the morning at work. Each person was asked where their first cup of coffee was brewed each morning: at home, at the office, national coffee shop, or locally owned coffee shop. Survey results show that 550 people said at home, 90 at the office, 90 at a national coffee shop, and 70 at a locally owed coffee shop. What is the probability that the first 5 people surveyed all brewed their first cup at home?
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