You have given us four digits. To rearrange them in all possible different ways: There are 4 choices for Digit-1, and for each of those ... there are 3 choices for Digit-2, and for each of those ... there are 2 choices for Digit-3, and for each of those ... there is only 1 choice left for Digit-4. So the total number of choices is: ( 4 x 3 x 2 x 1 ) = 24 BUT ... You can't tell the difference between the two '9's, so for every arrangement, there's another one that looks exactly like it, and you'd swear it's the same number. So the number of unique arrangements is only half of 24 = 12
With 123 digits you can make 123 one-digit numbers.
7 two-digit numbers.
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
None. 3 digit numbers are not divisible by 19 digit numbers.
500
With 123 digits you can make 123 one-digit numbers.
There are 5460 five digit numbers with a digit sum of 22.
27 three digit numbers from the digits 3, 5, 7 including repetitions.
There are 7,290 different 4-digit numbers that can be formed from the digits 1-9 without repetition.
7 two-digit numbers.
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
There are 90000 5-digit numbers.
757
None. 3 digit numbers are not divisible by 19 digit numbers.
There are 5*4*3 = 60 such numbers.
24
500