Four departments in an engineering college (ME, PE, CE and EE) contain 4 faculty members each, i.e. an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Each department also has 5 student coordinators. A panel of 4 members is to be constituted for a conference such that 1 faculty member is selected from each department, so that the final committee has an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Also, 10 student coordinators have to be selected and no restrictions exist for the selection of the student coordinators. In how many ways can the panel be constituted including the selection of the student coordinators?a)44 + 20C10b)44 andtimes; 20C10c)4! andtimes; 20C10d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

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Four departments in an engineering college (ME, PE, CE and EE) contain 4 faculty members each, i.e. an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Each department also has 5 student coordinators. A panel of 4 members is to be constituted for a conference such that 1 faculty member is selected from each department, so that the final committee has an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Also, 10 student coordinators have to be selected and no restrictions exist for the selection of the student coordinators. In how many ways can the panel be constituted including the selection of the student coordinators?

a)
4⁴ + ²⁰C₁₀
b)
4⁴ × ²⁰C₁₀
c)
4! × ²⁰C₁₀
d)
None of the above

Correct answer is option 'C'. Can you explain this answer?

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Four departments in an engineering college (ME, PE, CE and EE) contain...

The panel of faculty members can be constituted in 4! ways, as we need to select one faculty member from each department and the order matters.

For the student coordinators, we have 5 choices for each position, and since there are 10 positions to fill, the number of ways to select the student coordinators is 5^10.

Therefore, the total number of ways to constitute the panel including the selection of the student coordinators is 4! * 5^10.

This simplifies to 24 * 9765625 = 23437500.

Thus, the answer is b) 44.

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Four departments in an engineering college (ME, PE, CE and EE) contain 4 faculty members each, i.e. an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Each department also has 5 student coordinators. A panel of 4 members is to be constituted for a conference such that 1 faculty member is selected from each department, so that the final committee has an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Also, 10 student coordinators have to be selected and no restrictions exist for the selection of the student coordinators. In how many ways can the panel be constituted including the selection of the student coordinators?a)44 + 20C10b)44 × 20C10c)4! × 20C10d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Four departments in an engineering college (ME, PE, CE and EE) contain 4 faculty members each, i.e. an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Each department also has 5 student coordinators. A panel of 4 members is to be constituted for a conference such that 1 faculty member is selected from each department, so that the final committee has an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Also, 10 student coordinators have to be selected and no restrictions exist for the selection of the student coordinators. In how many ways can the panel be constituted including the selection of the student coordinators?a)44 + 20C10b)44 × 20C10c)4! × 20C10d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four departments in an engineering college (ME, PE, CE and EE) contain 4 faculty members each, i.e. an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Each department also has 5 student coordinators. A panel of 4 members is to be constituted for a conference such that 1 faculty member is selected from each department, so that the final committee has an HOD, an Associate Professor, an Assistant Professor and a Lecturer. Also, 10 student coordinators have to be selected and no restrictions exist for the selection of the student coordinators. In how many ways can the panel be constituted including the selection of the student coordinators?a)44 + 20C10b)44 × 20C10c)4! × 20C10d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.

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