Respuesta :
Answer:
11,880 different ways.
Step-by-step explanation:
We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.
We will use permutations for solve our given problem.
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex], where,
n = Number of total items,
r = Items being chosen at a time.
For our given scenario [tex]n=12[/tex] and [tex]r=4[/tex].
[tex]^{12}P_4=\frac{12!}{(12-4)!}[/tex]
[tex]^{12}P_4=\frac{12!}{8!}[/tex]
[tex]^{12}P_4=\frac{12*11*10*9*8!}{8!}[/tex]
[tex]^{12}P_4=12*11*10*9[/tex]
[tex]^{12}P_4=11,880[/tex]
Therefore, offices can be filled in 11,880 different ways.
