A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. to do this, he ranks the orchestra's 10 cellists an
d 16 violinists in order of musical proficiency. what is the ratio of the total cellist rankings possible to the total violinist rankings possible?
1 answer:
Ranking is very critical in this problem. Therefore, the most applicable mathematical theory is permutations.
Ranking possible for the cellists:
Needed cellists = 5
Total available cellists = 10
Possible number of rankings = 10P5 = 10!/(10-5)! = 30240
Ranking possible for the violinists:
Needed violinists = 5
Total available = 16
Possible number of rankings = 16P5 = 16!/(16-5)! = 524160
Therefore,
Ratio of rankings (cellists to violinists) = 30240/524160 = 3/52
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