Enter a number with two or more digits to generate its 4-digit combinations. Enter a number with 4 digits to obtain all its permutations.
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Combinations and Permutations Generator for 4-digit Lottery Games

The manipulation of 4-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 4-digit games and will present JavaScript programs to generate permutations and combinations of any numbers that you enter.

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Combinations of 4-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 4-digit games, combinations are very useful in order to list all the possible 4-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 4 elements - like 0246, 0468, 2468, etc. You can generate the 4-digit combinations of any number using our 4-digit combinations generator supplied further below.

Permutation of 4-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 4-digit number has obviously 4 elements and will result in 24, 12, 6, 4, or 1 possible permutations depending on whether the elements are repeated or not. So, permutation is simply the possible rearrangements of the elements.

A 4-digit number with no repeating digit has 24 possible permutations. For example, the permutations of the number "1234" are { 1234, 1243, 1423, 4123, 1324, 1342, 1432, 4132, 3124, 3142, 3412, 4312, 2134, 2143, 2413, 4213, 2314, 2341, 2431, 4231, 3214, 3241, 3421, 4321 }. If one of the digits is repeated, then the number of possible permutations becomes 12. For example, the permutations of the number "0012" are { 0012, 0021, 0201, 2001, 0102, 0120, 0210, 2010, 1002, 1020, 1200, 2100 }. If two of the digits are repeated, then the number of possible permutations becomes 6. For example, the permutations of the number "0011" are { 0011, 0101, 1001, 0110, 1010, 1100 }. If one of the digits is tripled, then the number of possible permutations becomes 4. For example, the permutations of the number "0001" are { 0001, 0010, 0100, 1000 }. If all the four digits are identical, then there is only one possible permutation.

You can generate the 4-digit permutations of any number using our 4-digit permutations generator supplied further below. However, if your state lottery has a combo play type of the 4-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 Staright. Unlike 3-digit games, some US 4-digit games, do not have a combo play, therefore the permutations generator might be handy.


4-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 3 digits, there will be no non-repeating digit combinations. For 2 digits, there will only be dual-doubles and one-tripled.

Interestingly, although you can find the list of all the possible combinations of 4-digit game numbers on another page of this site, you can also generate them here by entering 0123456789 and marking all the five options.

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

Mark which ones
to generate

Total =


4-digit Permutations Generator

To use this combinations generator, just enter a four 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 4-digit games that do not offer a combination (combo) type of play.

4-Digit Permutation generator
Enter a 4-digit number


Total =


All the 4-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 4-digit numbers there are, and what are all the possible 4-digit numbers?"

There are 10,000 possible 4-digit numbers and they are: 0000, 0001, 0002, 0003, 0004, ... , 9999. That is, just start from 0 and count up to 9999. Unlike the 3-digit combinations, we have not encountered any generating program. However, with a little more work, you can use the 3-digit combinations generator to generate all 4-digit combinations. Here is what you can do : generate all 3-digit combinations 10 times. So that you have 1000 numbers from 000 to 999 as the first set, the same numbers as the second set, and so on. To all the first 1000 numbers generated add 0 to the front so that you have 0000, 0001, etc. To all the second 1000 numbers generated add 1 to the front so that you have 1000, 1001, etc. To the third set add 2, and so on up to the 10th set to front of which you add a 9. The generator for 3-digit numbers can be found here.

Related pages:
US 4-digit lottery games
How to play 4-digit games
Grouping and odds of 4-digit numbers
4-digit combinations and permutations generator

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