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An online vendor requires that customers select a password that is a sequence of upper-case letters, lower-case letters and digits. A valid password must be at least 10 characters long, and it must contain at least one character from each of the three sets of characters. What is the probability that a randomly selected string with exactly ten characters results in a valid password

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Answer:

0.0283642

Step-by-step explanation:

Number of uppercase letters = 26

Number of lowercas = 26 alphabets = 10

Number of password characters = 10

Hence total number of passwords with exactly 10 characters (26 + 26 + 10) ^10 = 62^10 = 839299365868340224 passwords

Password with 10 strings, and having atleast one upper, lower and digit character :

26^1 * 26^1 * 10^1 * (26+26+10)^7 = 23806114737966080 (1 upper, lower and digit character, the remaining 7 could be any of them)

Probability = required outcome / Total possible outcomes

P(password with atleast 1 upper, lower and digit character) = 23806114737966080 / 839299365868340224

= 0.0283642

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