For the Jack password question, since computers today are distinguishing between UPPER case and lower case letters, would not the options for selecting the "letters" be both UPPER (=26) and lower (=26) as well as 0-9. This would give you 62 possible items to chose from. Also this would affect the combinations of the name JACK or Jack or jack. Maybe I over-thought the question but it does make for a different outcome.
You are absolutely correct. I made the assumption that case doesn't matter, but the result would be different if upper and lower case were considered different characters. Thanks!
Good catch. Based on that case matters, I think the new arrangement of Jack is permut(8, 8) = 40,320 and cell C3 would be permut(62, 4) = 13,388,280. So the new answer would be 40,320/13,388,280 = 0.003012 which isn't sensible. It would make sense for the probability to be even smaller. Possibly for Jack's arrangement in cell D9, it's permut(8, 4) since there are 8 possibilities, we choose 4. This is a smaller number than permut(4, 4), hence a smaller probability.
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For the Jack password question, since computers today are distinguishing between UPPER case and lower case letters, would not the options for selecting the "letters" be both UPPER (=26) and lower (=26) as well as 0-9. This would give you 62 possible items to chose from. Also this would affect the combinations of the name JACK or Jack or jack. Maybe I over-thought the question but it does make for a different outcome.
You are absolutely correct. I made the assumption that case doesn't matter, but the result would be different if upper and lower case were considered different characters. Thanks!
Good catch. Based on that case matters, I think the new arrangement of Jack is permut(8, 8) = 40,320 and cell C3 would be permut(62, 4) = 13,388,280. So the new answer would be 40,320/13,388,280 = 0.003012 which isn't sensible. It would make sense for the probability to be even smaller.
Possibly for Jack's arrangement in cell D9, it's permut(8, 4) since there are 8 possibilities, we choose 4. This is a smaller number than permut(4, 4), hence a smaller probability.
In the password example, there is cindition that it can be used only once... Doesnt it means that we can total n would be 36 then 34 then 34?