What is the Number of Possible Committees with Frank Included?

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SUMMARY

The discussion centers on calculating the number of possible committees that include a specific member, Frank, from a club of 18 members. To determine the number of committees of 5 members that include Frank, one must select 4 additional members from the remaining 17 members. This is represented mathematically as C174, which equals 238. The initial incorrect approach of subtracting C175 from C185 was clarified and corrected in the discussion.

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  • Understanding of combinatorial mathematics, specifically binomial coefficients.
  • Familiarity with the notation Cnr for combinations.
  • Basic knowledge of set theory and selection processes.
  • Ability to perform calculations involving combinations and permutations.
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Homework Statement



A club for 18 members, among them Frank. They'll pick out a komitee of 5 members.
(a. How many different komitees is produced? Easy, just the binom. 18 over 5.)

b, How many if Franks in? (The question)

Homework Equations



(Unarranged sortments with no takebacks)
binominalkoefficient nCr:
( p )
( r )
((p over r))

The Attempt at a Solution



18 over 5 minus 17 over 5?? No.
 
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for b. if Frank is always in, you have to choose only 4 members among the remaining 17, which is C^{17}_{4}, equivalent to your 18 over 5 minus 17 over 5.
 
Last edited:
ah, 17C4, thanks a bunch.
 

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