Question

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?

Answer 1

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.

$^nP_r=\frac{n!}{(n-r)!}$, where,

n = Number of total items,  

r = Items being chosen at a time.        

For our given scenario $n=12$ and $r=4$.

$^{12}P_4=\frac{12!}{(12-4)!}$

$^{12}P_4=\frac{12!}{8!}$

$^{12}P_4=\frac{12*11*10*9*8!}{8!}$

$^{12}P_4=12*11*10*9$

$^{12}P_4=11,880$

Therefore, offices can be filled in 11,880 different ways.