9.
∞ \ Infinite
Assuming the digits cannot be repeated, there are 7 combinations with 1 digit, 21 combinations with 2 digits, 35 combinations with 3 digits, 35 combinations with 4 digits, 21 combinations with 5 digits, 7 combinations with 6 digits and 1 combinations with 7 digits. That makes a total of 2^7 - 1 = 127: too many for me to list. If digits can be repeated, there are infinitely many combinations.
You can make: 1 combination containing 0 digits, 7 combinations containing 1 digits, 21 combinations containing 2 digits, 35 combinations containing 3 digits, 35 combinations containing 4 digits, 21 combinations containing 5 digits, 7 combinations containing 6 digits, and 1 combinations containing 7 digits. That makes 2^7 = 128 in all.
1000
45 In combinations, the order of the digits does not matter so that 12 and 21 are considered the same.
12, including a combination containing 0 digits.
10000
10
There are ten combinations: one each where one of the ten digits, 0-9, is excluded.
Since 0 cannot be in the first place of the 4-digits number, we have 9 x 10 x 10 x 10 = 9,000 combinations.
There are 13 combinations.
There are only 10 combinations. In each combination one of the 10 digits is left out.