Oh, dude, let me grab my calculator for this super thrilling math question. So, you've got 9 numbers and you're trying to figure out how many ways you can arrange them. That's like 362,880 combinations, but who's counting, right? Just a casual number of possibilities for your 9-digit number extravaganza.
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To calculate the number of 9-digit combinations that can be made from the numbers 1-9 without repetition, we use the permutation formula. Since there are 9 numbers and we are choosing 9 without repetition, the formula is 9P9 = 9! / (9-9)! = 9! / 0! = 9! = 362,880. Therefore, there are 362,880 9-digit combinations that can be made from the numbers 1-9.
If the numbers are not allowed to repeat themselves then 362,880.
* * * * *
That is the number of permutations, not combinations.
In a combination the order of the digits does not matter. So there is only one 9-digit combination.
If there are no restrictions on duplicated numbers or other patterns of numbers then there are 10 ways of selecting the first digit and also 10 ways of selecting the second digit. The number of combinations is therefore 10 x 10 = 100.
The answer is 10C4 = 10!/[4!*6!] = 210
Each digit can appear in each of the 4 positions. There are 9 digits, therefore there are 9⁴ = 6561 such combinations.
Through the magic of perms and coms the answer is 729
Using the formula n!/r!(n-r)! where n is the number of possible numbers and r is the number of numbers chosen, there are 13983816 combinations of six numbers between 1 and 49 inclusive.