If you consider each set of 4 digits as a unique code regardless of numeric order (the code 0123 would be counted as a different code than 0132, 0213, 0231, 0312, 0321, 1023, 1032, 1203, 1230, 1230, etc.), there are 3,528 possible codes in the base 10 system containing the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
720 (10*9*8)
Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.
5 digit telephone numbers having at least one of their digits repeated is = total possible 5 digit telephone numbers - 5 digit telephone numbers without any digit being repeated. =(10*10*10*10*10)-(10*9*8*7*6) =100000-30240 =69760
625 if numbers can have leading 0s, 500 otherwise.
823543
720 (10*9*8)
Using the digits of 1345678, there are 210 three digit numbers in which no digit is repeated.
There are 27 of them.
It is possible to create a 3-digit number, without repeated digits so the probability is 1.
5 digit telephone numbers having at least one of their digits repeated is = total possible 5 digit telephone numbers - 5 digit telephone numbers without any digit being repeated. =(10*10*10*10*10)-(10*9*8*7*6) =100000-30240 =69760
625 if numbers can have leading 0s, 500 otherwise.
757
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.
823543
3897
There are 5! = 120 such numbers.
81