UltraCAD Design, Inc

Calculator for Factorials, Permutations, and Combinations

This calculator is shown below. It will calculate the parameters for virtually any values. I have used it to calculate the factorial of 10,000,000,000! (But a factorial this large takes considerable time to calculate!)

10,000,000,000! = 2.80976134595865 * 10^(995657055186)

Accuracy is to about 12 significant digits, but the order of magnitude (10^x) should be exact.

Here is an explanation of the terms used:

Factorials: Factorials are pretty well understood. For example,

25! = 25*24*23*22*...*3*2*1 = 1.55112100433311 * 10^25

Permutations:  Permutations can be considered sampling without replacement but with regard for order.

For example, consider a deck of 52 cards. If we deal a hand of 5 cards, and we consider order to be important (i.e. A,K,Q,J,10 hearts is different from 10,J,Q,K,A hearts), there are 311,875,200 different permutations of hands that can be dealt. There are 52 ways the first card can be selected, 51 ways the second card can be selected, etc, down to 52 -5+1 ways (48 ways) the last card can be selected.

P(N,n) = N*(N-1)*(n-2)*...*(N-n+1)

(If order is not important, then this is a problem in combinations.)

Combinations:  Combinations can be considered sampling without replacement and without regard for order. This is the typical sampling type of problem.

C(N,n) = N!/[n!(N-n)!]

For example, if we deal five-card hands from a deck of 52 cards, there are 2,598,960 combinations of hands that can be dealt. If we draw samples of size 2 from a population of size 20, there are 190 samples (combinations) that can be drawn.

N^n:  This can be considered sampling with replacement and with regard for order.

For example, suppose I roll a six-sided die 4 times, there are 6*6*6*6 = 1,296 possible outcomes. But this would mean that a roll of 4,3,4,3 would be considered different from a roll of 4,4,3,3.

The Dice Problem:  Suppose I roll a six-sided die 4 times, but without regard for order. That is, an outcome of 4,4,3,3, is the same result as a 3,3,4,4. While there are 1,296 possible outcomes of rolling a die 4 times (6^4), there are only 126 possible different outcomes (without regard for order).

Note that this is the same problem as rolling 4 dice once. Each die can be considered an independent roll.


The tool requires a license to use. The license costs $30 for each licensee. If you purchase a license it will be sent to you by email in the form of a file (named combinations.dat). Place the license file in the same folder as the program executable. The program requires four files in that folder: the executable (Combinations.exe), the license file (Combinations.dat), the help file, Combinations.chm, and a license control file (ucadlic.dll).

Download the Combinations Tool Here.

Purchase a license here.

Operating System Requirements:

This calculator is designed to run on Windows 98/ME/NT/2K/XP/VISTA/Win7, 32 bit and 64 bit versions.


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