Combinations - multiplied sum of doubles, triples, quadruples.....

[gotthejazz]

Hi. I need to find the multiplied sum of double, triple, quadruple...
combinations in a row, both separately and combined.

e.g.
1 2 3 4
2 5 4 6

doubles (2*5)+(2*4)+(2*6)+(5*4)+(5*6)+(4*6)
triples (2*5*4)+(2*5*6)+(2*4*6)+(5*4*6)
....and so on...

Is there a way to do this in excel?
many thanks

 

[Dana DeLouis]

e.g.

1 2 3 4

Hi. Others have posted "Permutation" type programs here, and especially
over in the Excel Programming group.
As a side note, if your numbers were consecutive, as in your first
example, then maybe the following...
If you had 1,2,...20, and you wanted to use a Subset size of 2, then
perhaps: (A1 = 20)

=((A1-1)*A1*(1 + A1)*(2 + 3*A1))/24
Returns:
20,615

Other sizes than 2 require different equation.
I know this is not what you want, but your question got me thinking of a
old recurrence problem. I went back and totally rewrote it based on
some new programming ideas.
Given the numbers 1,2,...5000, take all the subsets of size 4. Multiply
each group of numbers, and add them up.
We note that there are Combin(5000,4) = 26,010,428,123,750 such subsets.
I got the time down to 0.0039 seconds. Yeah! :>)

Sub TestIt()
Dim t, m, n
m = 5000
n = 4
t = Timer
Debug.Print StirlingFirst(m + 1, m + 1 - n)
Debug.Print FormatNumber(Timer - t, 6)
End Sub

Returns a very large number:

1,016,438,775,060,761,172,309,114,625

0.003906

= = = =
Dana DeLouis

"To understand recurrence, one must first understand recurrence."
= = = =