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Unformatted text preview: ECEN 303: Assignment 1 Problems: 1. Following the argument presented in the notes, prove that parenleftBigg intersectiondisplay α ∈ A S α parenrightBigg c = uniondisplay α ∈ A S c α . 2. John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums? 3. For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9; the second digit was either 0 or 1; the third digit was any integer between 1 and 9. How many area codes were possible? How many area codes starting with a 4 were possible? 4. In how many ways can 8 people be seated in a row if (a) there are no restrictions on the seating arrangement; (b) persons A and B must sit next to each other; (c) there are 4 men and 4 women and no 2 men or 2 woman can sit next to each other;...
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 Fall '07
 Chamberlain
 Jack, Jay, Jim, c Sα

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