Problem #3 please There are 25 math majors, 35 civil engineering majors, and 40

Question

Problem #3 please

There are 25 math majors, 35 civil engineering majors, and 40 mechanical engineering majors at a school. How many ways are there to pick three representatives so that each major is represented? IIow many ways are there to pick one representative who is either a math major or a civil engineering major? A hotel has 20 floors each with 35 rooms. IIow many rooms are there in the hotel? A multiple choice exam has 20 questions. There are five possible answers for each question. How many ways can the answer key be written? How many ways can a student complete the exam? Students are allowed to leave questions blank. (a) How many three letter initials are possible? (b) How many three-letter initials are possible if none of the letters can be repeated? A national committee is to be comprised of a represenative from each of the fifty states, the District of Columbia, Puerto Rico, and Guam. For the states, the representative is either the governor or one of the two state senators. For DC, the representative is the mayor; for Puerto Rico, the representative is either the governor, the President of the Senate, the Speaker of the House, or the Chief Justice of the Supreme Court of Puerto Rico; and for Guam, it is the governor. How many committees are possible? How many ways can a supervisor with 25 employees select ten employees to be in a focus group if: Xavier and Yoda must be in the focus group; either Xavier or Yoda, but not both, must be in the focus group; neither Xavier nor Yoda are in the focus group. Every student in a particular Calculus class is either a math major, a computer science major, or both. If the class has 33 math majors (including double majors), 27 computer science majors (including double majors), and 15 double majors, how many students are there in the class? In a field of 10 evenly matched horses, how many ways are there for the horses to win, place, and show (first, second, and third place, respectively)? Eight candidates are running for Town Council. How many ways may their names be listed on the ballot?

Explanation / Answer

3.

A)

There are 5^20 = 9.53674*10^13 ways [ANSWER]

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B)

Now, it seems like there are 6 options for the student then.

Thus, there are 6^20 = 3.65616*10^15 ways [ANSWER]

  

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