Question: A string quartet consisting of two violinists, a violist, and a cellist. Suppose a group of six violinists, three violists, and two cellists are participating

A string quartet consisting of two violinists, a violist, and a cellist. Suppose a group of six violinists, three violists, and two cellists are participating in the member selections of a string quartet.

Consider the following scenarios:

A. In how many ways can the violinists of the string quartet be selected?

B. In how many ways can the violinists of the string quartet be selected if one of the violinists is to be designated as the first violinist and the other is to be designated as the second violinist?

Explain which type of counting principles (permutations or combinations) can be applied to each scenarios? (hint: does the order in which the violinists are selected matter? )

Which scenario has more counts ? Justify your answer.

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