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Re: Combinations

  • To: mathgroup at
  • Subject: [mg30787] Re: [mg30769] Combinations
  • From: "Michael" <michael at>
  • Date: Wed, 19 Sep 2001 00:16:26 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

> Hello.  I have Mathematica 4.1
> In a Program like Excel, or a hand-held calculator, one can return the
> number of combinations and permutations.
> However, I can not find an equivalent function in Mathematica.
> For example, Permutations[ ] returns a long list of all the "Actual"
> permutations.
> I am looking for just the final number.
> If there is one, could you include 'how' you found it.  I have looked
> everywhere.
> I know DiscreteMath`Combinatorica` has some stuff in it, but the Help
> appears not to explain many of them.
> I can write a custom function, but I am curious to find out if this
> is built in to Mathematica.
> I hope the answer is not to take the Length[ ]  of a rather long list.
> TIA.  Dana
> (I posted this question a month ago, but it never showed up in the
> newsgroup, or in the archives.
> I hope I am not doing something wrong.)

The number of permutations is simply Factorial[n] (n!).  A quick
double-check can be obtained by calling  following function with small
integers to see if you always get True:

verifyP[x_Integer] := Length[Permutations[Range[x]]] == x!

If you want to see how many ways you can take a subset of n items out of a
total of m items, you can use the Binomial function.  For example, how many
different ways can you choose 5 objects from 49?

In[26]:= Binomial[49, 5]
Out[26]= 1906884

Hope this helps.


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