The total number of possible 4-number combinations without repeating digits depends on whether the order of the numbers matters (permutations) or not (combinations).
- If order matters (permutations), such as forming 4-digit numbers with no digit repeated (digits from 0-9), there are 10×9×8×7=504010\times 9\times 8\times 7=504010×9×8×7=5040 possible combinations.
- If order does not matter (combinations), the number is given by the combination formula (104)=10!4!×6!=210\binom{10}{4}=\frac{10!}{4!\times 6!}=210(410)=4!×6!10!=210.
So:
- Permutations without repetition (order matters) = 5040
- Combinations without repetition (order does not matter) = 210
This distinction is important depending on the context of the question.
