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A computer programming team has 12 members.
(a) How many ways can a group of 7 (out of the 12 members) be chosen to work on a special project? Explain.
(b) Suppose that out of the 12 members on the team 7 are IT majors and 5 are math majors.
(i) How many groups of 7 people can be formed that contain 4 IT majors and 3 math majors? Explain.
(ii) How many groups of seven can be formed that contain a least 1 IT major? Explain.
(c) Suppose that two team members (of the 12 of either major) refuse to work together. How many groups of seven can be chosen to work on a project? Explain.
(d) Suppose that two team members insist on either working together or not at all on projects. (That is, either the two people both work on the project together or neither will work on the project.) How many groups of seven can be chosen to work on a project? Explain.
Let X be a finite dimensional linear space. Show that, for every subspace Y of X, Y perp perp = Y (that is, the annihilator of the annihilator of Y is Y)
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Grandy Company has 5,000 obsolete desk lamps that are carried in inventory at manufacturing costs of $50,000. If the lamps are reworked for $20,000, they could be sold for $35,000.
To make x thousand computer chips requires fixed expenditures of $352 plus $42 per thousand chips. Receipts from the sale of x thousand chips amount to $130 per thousand.
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