Enter a number with two or more digits to generate its 3-digit combinations. Enter a number with 3 digits to obtain all its permutations.
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Combinations and Permutations Generator for 3-digit Lottery Games

The manipulation of 3-digit games with regard to their various arrangements and groupings is performed by two mathematical tools called permutations and combinations. Here we will describe these two tools as applied to 3-digit games and will present JavaScript programs to generate permutations and combinations of any numbers that you enter.

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Combinations of 3-digit Games

The combinations of a number, a string, or any other set of objects with N elements is the possible grouping of the N elements into sub-groups of n elements. For example, the string 'bye' has 3 elements (that is N=3). If we want to group the three elements into sub-groups of 2 elements, then n will be 2. The resulting sub-groups will be {'be', 'by', 'ye'}. Certainly, the arrangements of the elements doesn't matter here; so, they might as well be {'eb', 'yb', 'ey'}.

In 3-digit games, combinations are very useful in order to list all the possible 3-digit numbers from numbers that have 2 or more digits. For example, if you may wish to play all even digits, then you'll have to group the five elements 02468 into sub-groups of 3 elements - like 024, 046, 268, etc. You can generate the 3-digit combinations of any number using our 3-digit combinations generator supplied further below.

Permutation of 3-digit Games

The permutations of a number, a string, or any other set of objects with N elements (or members) is the possible arrangements of its N elements. For example, if you consider the two-element string "NO", there are two possible permutations, namely, 'NO' and 'ON'. A 3-digit number has obviously 3 elements and will result in 6, 3, or 1 possible permutations depending on whether the elements are repeated or not. So, permutation is simply the possible rearrangements of the elements.

A 3-digit number with no repeating digit has 6 possible permutations. For example, the permutations of the number "123" are { 123,132,312,213,231,321 }. If one of the digits is repeated, then the number of possible permutations becomes 3. For example, the permutations of the number "001" are { 001,010,100 }. If all the three digits are identical, then there is only one possible permutation.

You can generate the 3-digit permutations of any number using our 3-digit permutations generator supplied further below. However, if your state lottery has a combo play type of the 3-digit game, then you do not need to generate any permutations. Note that the combo play type may be known by a different name in your state; it may be called Combination, Wheel Bet, Wheeled Play, Super Straight. Therefore, for US 3-digit games, you may not need to use the permutations generator.


3-digit Combinations Generator

To use this combinations generator, first enter a number with 2 or more digits. Then mark one or more of the three types of combinations (non-repeating digits, one-repeating, and triples) you want to generate. Finally press the 'Generate' button. The generated numbers will be listed in the box on the right. Note that if you enter 2 digits, there will be no non-repeating digit combinations.

Interestingly, although you can find the list of all the possible combinations of 3-digit game numbers on another page of this site, you can also generate them here by entering 0123456789 and marking all the three options.

3-Digit Combinations Generator
Enter a number
up to 10 digits long

Mark which ones
to generate

Total =


3-digit Permutations Generator

To use this permutation generator, just enter a three digit number and click on the 'Generate' button. The generated numbers will be listed in the box on the right.

Note that the permutations of numbers are necessary only for those 3-digit games that do not offer a combination (combo) type of play.

3-Digit Permutation generator
Enter a 3-digit number


Total =


All the 3-digit numbers

Finally, we have to add this section which we initially thought was trivial. In fact, amazingly many people ask the question "How many possible 3-digit numbers there are, and what are all the possible 3-digit numbers?"

There are 1000 possible 3-digit numbers and they are: 000, 001, 002, 003, 004, ... , 999. That is, just start from 0 and count up to 999. If you want the full list of all these numbers, you can find a number generator here.

Related pages:
US 3-digit lottery games
How to play 3-digit games
Grouping and odds of 3-digit numbers
Sum of 3-digit numbers

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