Question 1048825: Hi there, without writing out each possible way, could you show me how to figure this out please?
The horse committee of Green Solutions consists of 5 committee members. 12 people are interested in serving in the committee. How many different ways can the committee be selected? (Please Show work)
Thank you!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If the order in which the committee members were selected, then the number of permutations of 12 people selected 5 at a time is found by considering that there are 12 ways to choose the first member, and for each of those 12 ways to choose the first member there are 11 ways to choose the second member. That makes 132 ways to choose the first two members. Then, for each of those 132 ways to choose the first two members, there are 10 ways to choose the third member, making 1320 ways to choose the first three members. Continuing to analyze the situation in this manner gives us  ways to choose all 5 members (you can finish the arithmetic yourself).
However, the order in which the members are chosen doesn't matter because the committee consisting of Alice, Bob, Charlie, David, and Edith is exactly the same as the committee consisting of Bob, David, Charlie, Alice, and Edith. Hence the number we arrived at above is too large by a factor of the number of ways to arrange 5 different people, namely  (again, you do the arithmetic). So you have to divide the results of the computation in the first paragraph by the results of the computation in this paragraph. I'll let you handle that arithmetic, too.
In general, the number of ways to choose  things from a set of  things (also referred to as the number of combinations of things taken at a time) is given by:
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Where  (read: x factorial) is defined on the set of positive integers as \ \times\ x)
John
My calculator said it, I believe it, that settles it
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