Question

If you need 60 000 codes, how many digits long should each code be? There should be no repeated digits!

Answer 1

We want 60,000 n-digit numbers with no repeated digits.

Assuming that the code may begin with zero,
there are 10 choices for the first digit,
9 choices for the second digit,
8 choices for the third digit, etc.

We find that 10\times9\times8\times7\times6 = 30,240
. . . That is, there are only 30,240 five-digit codes.

We must use six-digit codes with 10\times9\times8\times7\times6\times5 = 157,200 permutat