Permutations up to 8 things


How many ways can we arrange several things in various repetitions in a certain number of boxes?
Enter a number <20 in at least a few of the boxes below:

The Number of possible arrangements is then:
of which one such arrangement is shown at right (click above again for a new arrangement). The number above is calculated from the following equation:

where n is the total number of things (n! means n factorial, so if you have 6 total objects this is 6*5*4*3*2*1), a is the number in box 1 (in this case 2 which is 2!=2*1, b is the number in box 2, c is the number in box 3 and so forth if you have more things to put in boxes (each box shows the number of each object in a box). Any n up to 100 is possible here, with a, b, c...h etc. adding up to 100 or less. Really cool formula. Try low numbers, even 0, and check me.
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