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A company president is deciding how to fill three vice-presidencies in the company: VP-Marketing. Vp- Finance, and VP-Production. Twelve executives are eligible and qualified for promotion. In how many wayscan the positions be filled?

Answer :

We have 12 candidates for a 3 positions.

In this case, the positions are different of each other (it is not the same be VP-Marketing or VP-Finance).

This situation can be modeled as a permutation, of 12 in 3.

[tex]\begin{gathered} _nP_r=\frac{n!}{(n-r)!} \\ _{12}P_3=\frac{12!}{(12-3)!}=\frac{12!}{9!}=12\cdot11\cdot10=1320 \end{gathered}[/tex]

Answer: The positions can be filled in 1320 different ways.

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