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Determine how many groups of a given number are in a entire set

  1. Jan 29, 2005 #1
    Hello all. I'm looking for an equation, one that I use to know how to figure out(but alas I am getting old and senile), that will alow me to determine how many groups of a given number are in a entire set.

    For example; in a set of 5, how many possible groups of 3 would there be? The answer is 10 sets of 3 in a set of 5.

    So, if anyone knows an equation for this, I would be very greatful. TIA.

  2. jcsd
  3. Jan 29, 2005 #2


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    You're thinking of a combination. If I write the combination of n things taken r at a time like this: C(n,r), the formula is:

    [tex] C(n,r) = \frac{n!}{r!(n-r)!} [/tex]

    So in your example:
    [tex] C(5,3) = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5\cdot 4}{2} = 10 [/tex]
  4. Jan 29, 2005 #3


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    How about this one??[itex] C_{5}^{3} [/itex]

    Did u study combinatorics in school??

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