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roncace science forum beginner
Joined: 04 Apr 2006
Posts: 2

Posted: Tue Apr 04, 2006 1:15 am Post subject:
Calculating how many m of n combinations in which an object appears



Say there are n objects taken m at a time. How can I determine the
number of times any single object, or any one of a subset of the
objects (size <= m) appears in the combinations. Here is an example of
what I mean:
There are 5 objects { a, b, c, d, e } and I want to look at the
combinations of those objects taken 3 at a time:
a b c
a b d
a b e
a c d
a c e
a d e
b c d
b c e
b d e
c d e
Now, how many of those combinations contain either a or b? For this
example the answer is nine, by actual count. Can anyone help me with a
general expression to solve this type of problem without enumeration of
all of the combinations?
Thanks!
Bob 

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JeanPierre LEVREL science forum beginner
Joined: 04 Apr 2006
Posts: 1

Posted: Tue Apr 04, 2006 1:15 am Post subject:
Re: Calculating how many m of n combinations in which an object appears



"roncace" <rroncace@yahoo.com> a écrit dans le message de news:
1144113312.990889.201290@z34g2000cwc.googlegroups.com...
 Say there are n objects taken m at a time. How can I determine the
 number of times any single object, or any one of a subset of the
 objects (size <= m) appears in the combinations. Here is an example of
 what I mean:

 There are 5 objects { a, b, c, d, e } and I want to look at the
 combinations of those objects taken 3 at a time:

 a b c
 a b d
 a b e
 a c d
 a c e
 a d e
 b c d
 b c e
 b d e
 c d e

 Now, how many of those combinations contain either a or b? For this
 example the answer is nine, by actual count. Can anyone help me with a
 general expression to solve this type of problem without enumeration of
 all of the combinations?

 Thanks!
 Bob

1) nombre de combinaisons de m éléments pris parmi n :
Nt = C(n,m) = n!/m!/(nm)!
ex : n = 5, m = 3 => Nt = 10
2) nombre de combinaisons contenant exactement un élément prédéfini :
N1 = C(n1,m1), mais aussi N1 = Nt  C(n1,m)
ex : n = 5, m = 1 => N1 = C(4,2) = 6 mais aussi N1 = 10  C(4,3) = 10  4 =
6
3) nombre de combinaisons contenant au moins un élément parmi k éléments
prédéfinis :
Nk = Nt  C(nk,m) =
ex : n = 5, m = 3, k = 2 => N2 = 10  C(3,3) = 10  1 = 9
autre exemple : n = 6, m = 3 =>
Nt = C(6,3) = 20
N1 = 20  C(5,3) = 10
N2 = 20  C(4,3) = 16
N3 = 20  C(3,3) = 1
JPL (from France) 

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roncace science forum beginner
Joined: 04 Apr 2006
Posts: 2

Posted: Tue Apr 04, 2006 1:34 pm Post subject:
Re: Calculating how many m of n combinations in which an object appears



JeanPierre;
Now I see it. Merci, beaucoup!
Bob 

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