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The math department at the Mathland Institute of Science consists of twenty-five professors and eighteen lecturers....

  1. The math department at the Mathland Institute of Science consists of twenty-five professors and eighteen lecturers.

a) In how many ways can the math department form a six-person committee if the committee must contain at least one lecturer?

b) In how many ways can the math department form a committee consisting of three professors and five lecturers?

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