with 4 numbers how many combinations are there

 with 4 numbers how many combinations are there

with 4 numbers how many combinations are there


The number of combinations possible with 4 numbers depends on whether repetition is allowed or not, and if order matters or not.
If repetition is allowed and order matters (permutations with repetition), then there are 4 options for the first number, 4 options for the second number, 4 options for the third number, and 4 options for the fourth number. Therefore, the total number of combinations is 4 x 4 x 4 x 4 = 256.


If repetition is not allowed and order matters (permutations without repetition), then there are 4 options for the first number, 3 options for the second number, 2 options for the third number, and 1 option for the fourth number. Therefore, the total number of combinations is 4 x 3 x 2 x 1 = 24.

If repetition is allowed and order does not matter (combinations with repetition), then there are 7 possible combinations of 4 numbers: (1) 4 identical numbers, (2) 3 identical numbers and 1 different number, (3) 2 identical numbers and 2 different numbers, (4) 2 identical numbers and 2 other identical numbers, (5) 2 pairs of identical numbers, (6) 1 identical number and 3 different numbers, and (7) 4 different numbers.

If repetition is not allowed and order does not matter (combinations without repetition), then there are 6 possible combinations of 4 numbers: (1) 4 different numbers, (2) 3 different numbers and 1 repeated number, (3) 2 different numbers and 2 different numbers, (4) 2 different numbers and 1 repeated pair, (5) 1 different number and 3 different numbers, and (6) 1 different number and 1 repeated triple.
Note: It's important to clarify the specific rules for combination or permutation in a given scenario, as this will determine the calculation of the total number of possible combinations.



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