In a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
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123480
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In a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
Total Applicants = 15
Violinists = 7
Cellists = 8
2 vacancies for cellists only = ⁸C₂ = 8!/(6!2!) = 28
4 vacancies for violinists only = ⁷C₄ = 7!/(4!3!) = 35
Remaining Musicians = 15 - 2 - 4 = 9
4 vacancies for any of these musicians = ⁹C₄ = 9!/(5!4!) = 126
Total number of ways these vacancies can be filled = 28 * 35 * 126 = 123480
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