HiBG5965.

First consider codes in which the first three digits are with Then For each except 0, there is exactly one such that is divisible by 10. Hence there are 9 such codes beginning with 0 allowed can be any digit except 0). There are also 9 such codes beginning with 5 allowed can be any digit except 5). For each code starting 1, 2, 3, 4, 6, 7, 8 and 9, there are 8 such codes allowed can be any digit except and So the total number of allowable security codes beginning is

The number of security codes beginning with is 10 × 9 = 90. Similarly for codes beginning with And the number of security codes in which the first three digits are distinct is 10 × 9 × 8 = 720.

Hence the total number of allowable security codes is 82 + 90 + 90 + 720 = 992.