Expert: Ahmed Salami - 8/13/2004

Question
Hello:

If I understand your reply correctly, are the following correct?

A proportion having 3 different proportion calculations would have 12 different combinations, a proportion having 4 different proportion calculations would have 16 different combinations, a proportion having 5 different proportion calculations would have 20 different combinations, a proportion having 6 different proportion calculations would have 24 different combinations, etc.

I thank you for your follow-up reply.
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Followup To
Question -
Hello:

If a proportion such as a/b = c/d has eight different proportion calculations, how many different combinations of proportion
calculations are possible with a proportion having 3 ratios as in
a/b = c/b = e/f, a proportion having four ratios a/b = c/d = e/f =
g/h, and etc.?

Example for a/b = c/d

a/b = c/d
b/a = d/c
c/d = a/b
d/c = b/a
a/c = b/d
c/a = d/b
b/d = a/c
d/b = c/a


I think, but I'm not sure, that the proportion having three ratios may have 24 different combinations.


Does a pattern begin to develop in regards to the number of different combination of ratios in a proportion having a different number of ratios?
If so, what is it?

I thank you for your reply.

Answer -
Hello,
If we are talking of combinations, then I think that the first and third options in your example are the same, so there is only half as much combinations for the two proportions.
For n proportions, there are nC2(read "n combination 2")ways of selecting in twos. Each selection would now have 4 different combinations each. So there would be a total of 4.nC2 ways.

For example, with 3 ratios we have 4.3C2 = 4.3 = 12 combinations.

Hope its all good.
Regards.

Answer
Hi,
No, they aren't.
I gave you the formula 4. nC2
nCr = n!/(n-r)!r!
So, nC2 = n!/(n-2)!2!
where n! = n(n-1)(n-2)......3.2.1
So for instance,
4C2 = 4!/2!2! = 4x3x2x1/(2x1)(2x1)= 24/4 = 6
Therefore, for 4 ratios there are 4.6 = 24 ways
and not 16. There should be around 40 ways for 5 ratios.
The others are done in the same way. You could also go through the pains of checking it by doing it without the formula and see what happens.
I hope you now get it.
Regards.