(1.) Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. (a) How many strings of hexadecimal digits consist of from one through four digits? (b) How many strings of hexadecimal digits consist of from two through six digits? (2.) 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 !, @, #, $, %, ^, &, *, (, ), −, +, {, and }. (a) How many passwords are possible if the repetition of symbols is allowed? (b) How many passwords contain no repeated symbols? (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? (Round your answer to the nearest tenth of a percent.)
(1.) Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. (a) How many strings of hexadecimal digits consist of from one through four digits? (b) How many strings of hexadecimal digits consist of from two through six digits? (2.) 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 !, @, #, $, %, ^, &, *, (, ), −, +, {, and }. (a) How many passwords are possible if the repetition of symbols is allowed? (b) How many passwords contain no repeated symbols? (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? (Round your answer to the nearest tenth of a percent.)
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 22E: License Plate Numbers In a certain state, each automobile license plate number consists of two...
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(1.)
Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
(a)
How many strings of hexadecimal digits consist of from one through four digits?
(b)
How many strings of hexadecimal digits consist of from two through six digits?
(2.) 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 !, @, #, $, %, ^, &, *, (, ), −, +, {, and }.
(a)
How many passwords are possible if the repetition of symbols is allowed?
(b)
How many passwords contain no repeated symbols?
(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? (Round your answer to the nearest tenth of a percent.)
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