I calculated the answer to the following question to be:
30664510802988210000

Question:
Of the 100 people in the US Senate, 18 serve on the Foreign Relations
Committee.  How many ways are there to select Senate members for this
committee (assuming party affiliation is not a factor in selection)?

I used nCr=n!/(n-r)!r!

100c18=100!/(100-18)!18!
=30664510802988210000

I am not sure if this is right, and just want some clarification.

---

Request for Question Clarification by mvguy-ga on 19 Nov 2006 17:37 PST

Would an answer to 14 significant digits be sufficient?

---

Clarification of Question by unknownentity-ga on 19 Nov 2006 17:40 PST

Most likely; I just need to use it to see where and if I went wrong with my math.

Hi!!


This is a counting problem, specifically an unordered selection:
"Ordered Selection:
...
In general, the number of ordered selections of m items out of n items is:

n!/(n-m)!
 
The idea is that we cancel off all but the first m factors of the n! product.

Unordered Selection:
...
In general, to choose (unordered selection) m candidates from n, there are:
              
n!/(n-m)!n! 
              
ways. We took the formula for ordered selections of m candidates from
n, and then divided by m! because each unordered selection was counted
as m! ordered selections.
..."
From "HSE Basic counting - Wikibooks, collection of open-content textbooks":
http://en.wikibooks.org/wiki/HSE_Basic_counting


The Unordered Selection is the selection that fits this problem, so
you have used the correct formula:
100!/(100-18)!18! = 100!/82!18! =
                  = 3.06645108029882083E+19 =
                  = 30664510802988208300


Your math for this problem is right.

For further references see:
"Permutations and Combinations":
http://cms.dt.uh.edu/faculty/delavinae/F05/2305/PermNComb.PDF

"Permutations and Combinations" by Joe Sawada:
http://www.cis.uoguelph.ca/~sawada/2910/notes/perms-1x2.pdf


Search strategy:
"How many ways are there to select"
permutations combinations


I hope this heps you. Feel free to request for a clarification if you need it.


Regards,
livioflores-ga

You're brilliant. :-)

I didn't multiply it out but your formula is correct.

I'm 95 percent that your formula is correct. If it is correct, your
multiplication is correct. The answer I get using your formula is
3.0664510802988 x 10^19, which is what you have. But I'm not certain
enough that you have the right formula to charge you for an answer.