SOLUTION: A city council with nine members must appoint a three person subcommittee. How many subcommittees are possible?

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Question 473736: A city council with nine members must appoint a three person subcommittee. How many subcommittees are possible?
Found 3 solutions by ewatrrr, ccs2011, Tanvi:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

A city council with nine members must appoint a three person subcommittee. 

How many subcommittees are possible? 9C3 = 84 possible subcommittees

Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
This will be solved using combinations because there is no order within the sub-committees.
How many groups of 3 can be made from 9 members.
Combination formula:
9C3 = 9%21%2F%28%289-3%29%21%2A3%21%29+=+9%21%2F%286%21%2A3%21%29
9! can be written as 9*8*7*6!
Notice that the 6! can be cancelled on top and bottom, leaving
%289%2A8%2A7%29%2F%283%2A2%2A1%29
You can simplify things by doing more cancelling, 9%2F3+=+3, 8%2F2+=+4
=3%2A4%2A7+=+12%2A7+=+84
Therefore there are 84 sub-committees possible.

Answer by Tanvi(1) About Me  (Show Source):
You can put this solution on YOUR website!
5*4*3/3*2*1
10