We treat this as a permutations and combinations problem... as there are two possible 'rules' involved.
If we are allowed to repeat a digit (such as 456537 - which as two 5s in it) then there are 9 options for every digit. So 9 x 9 x 9 x 9 x 9 x 9 = 531441 different six-digit numbers from a choice of 9.
If we cannot repeat a digit, as we did above, thee need to pick the first number - and it can be any of the 9.. then the second number can be any of 8, and the third can be any of 7 and so on.... this is called permutations and we end up with a multiplication like before but with each figure lower than the one before it.... 9 * 8 * 7 * 6 * 5 * 4 = 60480 different permutations of six digits from a choice of 9.
Number of 7 digit combinations out of the 10 one-digit numbers = 120.
56 combinations. :)
The answer will depend on how many digits there are in each of the 30 numbers. If the 30 numbers are all 6-digit numbers then the answer is NONE! If the 30 numbers are the first 30 counting numbers then there are 126 combinations of five 1-digit numbers, 1764 combinations of three 1-digit numbers and one 2-digit number, and 1710 combinations of one 1-digit number and two 2-digit numbers. That makes a total of 3600 5-digit combinations.
5,040
There are 840 4-digit combinations without repeating any digit in the combinations.
Number of 7 digit combinations out of the 10 one-digit numbers = 120.
56 combinations. :)
The answer will depend on how many digits there are in each of the 30 numbers. If the 30 numbers are all 6-digit numbers then the answer is NONE! If the 30 numbers are the first 30 counting numbers then there are 126 combinations of five 1-digit numbers, 1764 combinations of three 1-digit numbers and one 2-digit number, and 1710 combinations of one 1-digit number and two 2-digit numbers. That makes a total of 3600 5-digit combinations.
10,000
15
10!/3! = 604800 different combinations.
To find the number of 5-digit combinations from 1 to 20, we first calculate the total number of options for each digit position. Since the range is from 1 to 20, there are 20 options for the first digit, 20 options for the second digit, and so on. Therefore, the total number of 5-digit combinations is calculated by multiplying these options together: 20 x 20 x 20 x 20 x 20 = 3,200,000 combinations.
5,040
You would get 4!/2! = 12 combinations.
There are 840 4-digit combinations without repeating any digit in the combinations.
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.
If you can repeat the numbers within the combination there are 10,000 different combinations. If you cannot repeat the numbers within the combination, there are 5040 different combinations.