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by dtweah » Tue May 12, 2009 6:18 am
The City Council has nine members, who serve on different committees. Each committee has
three members and no two members serve together on more than one committee. Determine the
largest possible number of committees.

a. 9
b. 10
c. 12
d. 13
e. 24
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by avenus » Wed May 13, 2009 4:05 pm
Total number of possible committees 9C3
Every group of two people comes up in 7 different 3-people groups so:

9C3/7 = 12

Answer is C
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by dtweah » Wed May 13, 2009 4:29 pm
avenus wrote:Total number of possible committees 9C3
Every group of two people comes up in 7 different 3-people groups so:

9C3/7 = 12

Answer is C
Avenues please expound on the above particularly "Every group of two people comes up in 7 different 3-people groups ". I am more interested in the logic than the answer. What led you to 7? Can you build up an argument in a clear way?
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by avenus » Thu May 14, 2009 5:08 am
dtweah wrote: Avenues please expound on the above particularly "Every group of two people comes up in 7 different 3-people groups ". I am more interested in the logic than the answer. What led you to 7? Can you build up an argument in a clear way?
Sure. 9 people; take 2 of them as the first members of the committee. you have 7 left to choose from for the last member ==> Every pair will appear in 7 of all the possible options. Since we don't want them to be together in more than one committee, we have a 1:7 ratio, so you divide by 7.

does that help?
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