SOLUTION: Find the number of ways in which a committee, its chairman and its president can be selected from a set of n people. A person can be chairman as well as president. Committee can

Algebra ->  Permutations -> SOLUTION: Find the number of ways in which a committee, its chairman and its president can be selected from a set of n people. A person can be chairman as well as president. Committee can       Log On


   

Question 990529: Find the number of ways in which a committee, its chairman and its president can be
selected from a set of n people. A person can be chairman as well as president. Committee
can have any number of people?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Choose the chairman any of n ways.
Choose the president any of n ways. 
That's nē ways to choose the chairman and president.
For each of the remaining n-2 people, we can make two choices, either

1. to choose him/her to serve on the committee, or 
2. to choose him/her not to serve on the committee.

That's 2n-2, counting the cases where only the chairman and
president make up a 2-member committee.

Answer: n2*2n-2, assuming it is possible to choose
nobody else but the chairman and president.  Otherwise the answer is
n2*(2n-2-1), where we must have at least one other person.   You'll have 
to ask your teacher whether or not 2-member committees are to be counted.

Edwin