BIGNUM CALCULATOR

If the browser says the script is slowing the page, let it continue.
It is calulating your results, and should finish within one minute.
Calculates to 100 factorial. No fractions.
0 or -1 appears if calculation is not possible.
Sum: n+r
Difference: n−r
Product: n*r
Quotient: n/r
Remainder: n mod r
Power:
Value range:  
  replaced
  ordered
nr
Factorial:
Value range:  
  discarded
  ordered
n!
 
Permutation:
Value range:  
  discarded
  ordered
P(n,r)
 
Combination:
Value range:  
  discarded
  unordered
C(n,r)
 
Recombination:
Value range:  
  replaced
  unordered
R(n,r)
= C(n+r−1,r)

EXPLANATION

The Bignum Calculator is a Javascript program that uses arrays to calculate numbers beyond the normal reach of hand calculators and computer programs.

The following are explanations of some of the features:


An Explanation of Recombination Probabilities

What happens if the first color and the second color are chosen independently:

 First Color
Second ColorREDGREENBLUE
REDRedYellowMagenta
GREENYellowGreenCyan
BLUEMagentaCyanBlue

If the first color and the second color are chosen independently, the probabilities if the colors are:

The different colors have different probabilities. All of the table posuition outcomes are equally likely, but the same color can appear in multiple outcomes. Thus, some colors are more likely than others.

The following method produces equally likely outcomes for all colors:

Use R(n,r) to find the number of possible colors. To find out what the colors are, use the table above, and cross off the duplicate colors.

Make the table below, using the list of colors found, and placing to the right of each color only ONE way to mix that color.

Randomly choose one color from the left column. Then install the colors found in the other columns.

The order the colors are installed in the beams does not matter.

Color ChosenColors Installed
RedREDRED
YellowREDGREEN
GreenGREENGREEN
CyanGREENBLUE
BlueBLUEBLUE
MagentaREDBLUE

The above method produces the following colors in the following probabilities:

Now all of the colors have the same probabilitiies.