For a password that is 6 digits long and can contain numbers (0-9) and letters (

Question

For a password that is 6 digits long and can contain numbers (0-9) and letters (uppercase and lowercase are separate characters) of 62 possible characters total.

a.      What is the probability that the password will contain at least 2 capital letters

b.      What is the probability that the password will be made up of 6 different characters.

For the first one I think it is something along the lines of 1 - P(0) - P(1). Where P(0) and P(1) are the probabilities of the password containing no capitals and 1 capital respectively. To calculate P(0) you figure out the total number of combinations containing no capitals and divide it by the total number of combinations, and the same for P(1). I think I have figured out the total number of combinations: 62!/((62-6)!*6!, but am not sure about how to figure the number of combinations with 0 or 1 capital.

For the 2nd problem I really don’t know where to begin. I appreciate any help, thank you.

Explanation / Answer

a. P(0 or 1 capitals) = 36C6/62C2 + 36C5*26C1/62C2 = 0.1911, so P(2 or more) = 1-0.1911 = 0.8089 b. (62/62)(61/62)(60/62)(59/62)(58/62)(57/62) = 0.7793 the first one can be anything, the second one can be anything except for whatever the first thing was, etc.

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