1. a) Compute (1/2), (3), () without a calculator or computer program. b) For any positive...

  

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1. a) Compute (1/2), (3), () without a calculator or computer program. b) For any positive integers r, k, show that (7) = (1)* (*+k1). 2. Use Newton's binomial theorem to approximate 72/3 up to the cubic term. 3. Use the Inclusion-Exclusion Principle (Corollary 6.12) to count the number of r- combinations of 1, 2, ..., n containing 1 or 2 or 3. 4. A bakery sells chocolate, cinnamon, and plain doughnuts and at a particular time has 6 chocolate, 5 cinnamon, and 4 plain doughnuts. If a box contains 12 doughnuts, how many different options are there for the box? 1. a) Compute (1/2), (3), () without a calculator or computer program. b) For any positive integers r, k, show that (7) = (1)* (*+k1). 2. Use Newton's binomial theorem to approximate 72/3 up to the cubic term. 3. Use the Inclusion-Exclusion Principle (Corollary 6.12) to count the number of r- combinations of 1, 2, ..., n containing 1 or 2 or 3. 4. A bakery sells chocolate, cinnamon, and plain doughnuts and at a particular time has 6 chocolate, 5 cinnamon, and 4 plain doughnuts. If a box contains 12 doughnuts, how many different options are there for the box?