Combinations and Permutations Generator for 4digit Lottery Games
The manipulation of 4digit 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 4digit games and will present JavaScript programs to generate permutations
and combinations of any numbers that you enter.

On this page...

Combinations of 4digit 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 subgroups of n elements. For example, the string 'bye' has 3 elements (that is N=3). If we want
to group the three elements into subgroups of 2 elements, then n will be 2. The resulting subgroups 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 4digit games, combinations are very useful in order to list all the possible 4digit 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 subgroups of 4 elements  like 0246, 0468, 2468, etc. You can generate the 4digit
combinations of any number using our 4digit combinations generator supplied further below.
Permutation of 4digit 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 twoelement string "NO",
there are two possible permutations, namely, 'NO' and 'ON'. A 4digit 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 4digit 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 4digit permutations of any number using our 4digit permutations generator supplied further below.
However, if your state lottery has a combo play type of the 4digit 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 3digit games, some US 4digit games, do not have a combo play, therefore the permutations generator might be handy.
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4digit 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 (nonrepeating digits,
onerepeating, 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 nonrepeating digit combinations.
For 2 digits, there will only be dualdoubles and onetripled.
Interestingly, although you can find the list of
all the possible combinations of 4digit game numbers on another page of this site, you can also
generate them here by entering 0123456789 and marking all the five options.


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4digit 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 4digit games that do not
offer a combination (combo) type of play.


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All the 4digit 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 4digit numbers there are, and what are all the possible 4digit numbers?"
There are 10,000 possible 4digit numbers and they are: 0000, 0001, 0002, 0003, 0004, ... , 9999. That is, just start from 0 and count
up to 9999. Unlike the 3digit combinations, we have not encountered any generating program. However, with a little more work,
you can use the 3digit combinations generator to generate all 4digit combinations. Here is what you can do : generate all 3digit
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 3digit numbers can be found here.
Related pages:
• US 4digit lottery games
• How to play 4digit games
• Grouping and odds of 4digit numbers
• 4digit combinations and permutations generator

