Any 5 from 9 in any order = factorial 9 divided by factorial (9 - 5), ie 9 x 8 x 7 x 6 x 5 = 15120.
the repeated digits can lie in any of 3 positions:XXYZ,YXXZ, or YZXXTherefore, the number of different possible repeated digit combinations is 10×3=30 (there are 10 different possible digits).There are then 9 values left that Y could be, after the X's have their values, and 8 values left that Z could be, to ensure no unintended repeated numbers.This gives (10×3)×9×8=2160. There are therefore 2160 possible codes.
There are 210 4 digit combinations and 5040 different 4 digit codes.
There are 4 possible numbers if the digits are not repeated; 18 if they are. Those are 3-digit numbers, assuming that zero would not be a leading digit. If zero is allowed for a leading digit, then you can have 6 for the non repeated, and 27 if repetition.
Proceed from left to right, using the largest possible digit in each position.
1 set
If you include 0000, ten thousand unique four digit codes are possible.
100,000 - Every number from 00000 to 99999.
10*9*8*7*6=30,240
There are 900 possible three-digit numbers not beginning with 0. (Note, however, that this question does not accurately describe the restrictions on numbers that can be used as area codes.)
As far as I can tell, all 5 digit numbers are potential zip codes, so there are 99999 + 1 potential zip codes, or 100,000. Many of these are not actually is use.
6,720 combinations.
If a digit can be repeated there are 5 x 5 x 5 = 125 possible numbers If a digit cannot be repeated there are 5 x 4 x 3 = 60 possible numbers.
Any 3 from 10 in any order = 10 x 9 x 8 = 720It depends on what other restrictions you place on the numbers. For example, in North America (country code +1 = USA, Canada, etc.), area codes cannot have 0 or 1 as the first digit, and cannot have 9 as the second digit.
The number of 3-digit numbers with no repeated digits is simply 10x9x8 = 720, if you allow, for example, 012 as a 3-digit number. There are 10 digits, any of which might be the first digit. The second digit can be any digit except the digit that was used for the first digit, leaving 9 possibilities. The third digit then has 8 possibilities, since it can't be the same as the first or second digit. The actual number of possible area codes will be lower, because there are additional restrictions on the number combinations for a valid area code. For example, in North America (USA, Canada, etc.), the first digit of an area code cannot be 0 or 1 and the middle digit cannot be 9.
the repeated digits can lie in any of 3 positions:XXYZ,YXXZ, or YZXXTherefore, the number of different possible repeated digit combinations is 10×3=30 (there are 10 different possible digits).There are then 9 values left that Y could be, after the X's have their values, and 8 values left that Z could be, to ensure no unintended repeated numbers.This gives (10×3)×9×8=2160. There are therefore 2160 possible codes.
There can be 103 = 1000 codes.
81