Question

At a certain company, passwords must be from 3–5 symbols long and composed from the 26 uppercase letters of the Roman alphabet, the ten digits 0–9, and the 14 symbols !, @, #, $, %, ^, &, *, (, ), 2, 1, {, and }. c. How many passwords have at least one repeated symbol? d. What is the probability that a password chosen at random has at least one repeated symbol?

Answer 1

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Answer:

c)

The pass word must be from 3 to 5 symbols.

Number of passwords of length 3 is number of passwords of length 4 is and number of passwords of length 5 is

The total number of passwords is:

Therefore, there are passwords with the repetition of symbols.

The pass word must be from 3 to 5 symbols.

The number of passwords of length 3 is:

The number of combinations of length-3 with no repeated symbols is:

The number of passwords of length 4 is:

The number of combinations of length-4 with no repeated symbols is:

The number of passwords of length 5 is:

The number of combinations of length-5 with no repeated symbols is:

The number of passwords that contains no repeated symbols is:

Therefore, there are passwords with no repeated symbols.

The objective is to determine the number of passwords that have at least one repeated symbol.

The number of passwords with at least one repeated symbol is:

Thus, there are number of passwords that have at least one repeated symbol.

d)