SOLUTION: A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be fil

Algebra ->  Permutations -> SOLUTION: A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be fil      Log On


   

Question 1094501: A certain committee consists of
18
people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these
3
offices be filled? Assume that a committee member can hold at most one of these offices.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

This is a simple application of the fundamental counting principle.

There are 18 choices for the first officer chosen; it doesn't matter which office it is.
Then there are 17 choices left for the second officer chosen; then there are 16 choices left for the third officer chosen.

So the number of ways the offices can be filled is
18*17*16

Clearly, this is the permutation 18P3. However, I see too many students who think every problem like this is purely either a combination or a permutation, so I encourage you to think of it simply as an application of the fundamental counting principle.