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A club elects a​ president, vice-president, and​ secretary-treasurer. How many sets of officers are possible if there are 12 members and any member can be elected to each​ position? No person can hold more than one office.

Respuesta :

samuelonum1

Answer:

1320 sets

Step-by-step explanation:

 This problem brothers on selection without repetition, so we will be using permutation to solve this problem.

Given

n= 12 ,which is  the number we are choosing from

r= 3, which is the number of committee(president, vice-president, and​ secretary-treasurer.)

[tex]= \frac{n!}{(n-r)!}[/tex]

Substituting we have

[tex]= \frac{12!}{(12-3)!}\\\\ = \frac{12!}{(9)!}\\\\= \frac{12*11*10*9!}{9!}[/tex]

[tex]= 12*11*10= 1320[/tex]

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