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This seems to me as a more natural meaning of isogram but that wasn't your question. As for your bank can the 8 digit random number have its leading digit as zero? For example is 07569232 allowed? If so there are 10 choices for the first digit, 10 choices for the second digit and so on so the bank's random number generator is choosing form \[10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10^8\] possibilities. If an 8 digit "isogram" can also start with a zero then there are 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit and so on. This gives \[10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3\] 8 digit "isograms". Hence the probability that the bank will present you with an "isogram" is \[\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{10^8}\] I had Google do this calculation for me. I typed (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3)/(10^8) into the Google search window and Google responded with 0.018144 or a little less than two in a hundred. Harley
 


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