SOLUTION: A committee of 8 people are to choose a president, vice president, and a treasurer. If each officer is to be held by one person and no person is to hold more than one office, in ho

Algebra ->  Permutations -> SOLUTION: A committee of 8 people are to choose a president, vice president, and a treasurer. If each officer is to be held by one person and no person is to hold more than one office, in ho      Log On


   

Question 686400: A committee of 8 people are to choose a president, vice president, and a treasurer. If each officer is to be held by one person and no person is to hold more than one office, in how many ways can this committee be selected?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We can choose any one of the 8 people to be the
president.

That leaves 7 people to choose one out of to be the 
vice president.  

So for each of the 8 ways we can choose the president,
there are 7 ways we can choose the vice president.  

Therefore there are 8×7 or 56 ways we can choose the 
president and the vice president.

That leaves 6 people to choose one out of to be the 
treasurer.

So for each of the 8×7 or 56 ways we can choose the president
and the vice president, there are 6 people from whom we can 
choose to be the treasurer.  

Therefore there are 8×7×6 or 336 ways we can choose the 
president,the vice president, and the treasurer.  

That's the number of permutations of 8 things taken 3 at a
time.  ORDER MATTERS because president, vice-President,
and secretary are ordered by rank.

P(8,3) = 8×7×6 = 336

Edwin