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.Com
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(20055)   (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
RELATED QUESTIONS

A committee of 8 people randomly chooses 3 people to be president, vice president, and... (answered by stanbon)
A committee of 8 people randomly chooses 3 people in order to be president, vice... (answered by Alan3354)
In how many ways can a twenty-person club choose three different people to be president,... (answered by stanbon)
A committee consists of a President, a Vice President, a Treasurer, and a Secretary. The (answered by jorel1380)
A club with eighteen members is to choose three​ officers: ​ president,... (answered by ikleyn)
A club with 13 members is to choose three​ officers: ​ president, vice-president,... (answered by ikleyn)
how many ways can a president, vice-president, treasurer, and secretary be chosen from a... (answered by ikleyn)
If a committee of 3 is to be chosen at random from a class of 13 students, what is the... (answered by Edwin McCravy)
a club elects a president, vice-president, and secretary-treasurer. How many sets of... (answered by ikleyn)