If a leading zero is allowed...
The first digit can be 0-9, ten possibilities.
The second digit can be 0-9, ten possibilities.
The third digit can be 0-9, ten possibilities.
The fourth digit can be 3-9, 7 possibilities.
So there are 10x10x10x7 = 7000 such codes.
If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.
64 if repetition is allowed.24 if repetition is not allowed.
64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.
10^7 if the repetition of digits is allowed. 9*8*7*6*5*4*3 , if the repetition of digits is not allowed.
To form a two-digit number using the digits 0-9 without repetition, the first digit (the tens place) can be any digit from 1 to 9 (9 options), since a two-digit number cannot start with 0. The second digit (the units place) can then be any of the remaining 9 digits (including 0 but excluding the first digit). Therefore, the total number of two-digit numbers that can be formed is 9 (choices for the first digit) multiplied by 9 (choices for the second digit), resulting in 81 possible two-digit numbers.
If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.
If repetition of digits is allowed, then 56 can.If repetition of digits is not allowed, then only 18 can.
64 if repetition is allowed.24 if repetition is not allowed.
24 three digit numbers if repetition of digits is not allowed. 4P3 = 24.If repetition of digits is allowed then we have:For 3 repetitions, 4 three digit numbers.For 2 repetitions, 36 three digit numbers.So we have a total of 64 three digit numbers if repetition of digits is allowed.
64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.64 if repetition is allowed, 6 otherwise.
5040
10^7 if the repetition of digits is allowed. 9*8*7*6*5*4*3 , if the repetition of digits is not allowed.
5 ^12
0123456789
To form a two-digit number using the digits 0-9 without repetition, the first digit (the tens place) can be any digit from 1 to 9 (9 options), since a two-digit number cannot start with 0. The second digit (the units place) can then be any of the remaining 9 digits (including 0 but excluding the first digit). Therefore, the total number of two-digit numbers that can be formed is 9 (choices for the first digit) multiplied by 9 (choices for the second digit), resulting in 81 possible two-digit numbers.
It is 10000.
125