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Q1. In the following, explain using the multiplicative principle. You do not need to explicitly evaluate expressions involving factorials, exponents, or fractions. (i) How many functions are there from {1,2,..., 12} to {A, B, C,..., X, Y, Z}? (ii) What is the probability that a randomly chosen function from {1,2,..., 12} to {A, B, C,..., X, Y, Z} is one-to-one?

Q1. In the following, explain using the multiplicative principle. You do not need to explicitly evaluate expressions involving factorials, exponents, or fractions. (i) How many functions are there from {1,2,..., 12} to {A, B, C,..., X, Y, Z}? (ii) What is the probability that a randomly chosen function from {1,2,..., 12} to {A, B, C,..., X, Y, Z} is one-to-one?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q2. A software company is considering the format of its login passwords. Which of the following formats gives the largest number of possible passwords? Justify your answer using the multiplicative principle. (I) Three lower-case letters, followed by three upper-case letters, followed by three digits. (II) Eight lower-case letters. (III) Five lower-case letters followed by five digits. (Letters are chosen from the English alphabet of 26 letters. Digits are chosen from {0, 1,...,9}.)
Transcribed Image Text:Q2. A software company is considering the format of its login passwords. Which of the following formats gives the largest number of possible passwords? Justify your answer using the multiplicative principle. (I) Three lower-case letters, followed by three upper-case letters, followed by three digits. (II) Eight lower-case letters. (III) Five lower-case letters followed by five digits. (Letters are chosen from the English alphabet of 26 letters. Digits are chosen from {0, 1,...,9}.)
Q1. In the following, explain using the multiplicative principle. You do not need to explicitly evaluate expressions involving factorials, exponents, or fractions. (i) How many functions are there from {1,2,..., 12} to {A, B, C, ..., X, Y, Z}? (ii) What is the probability that a randomly chosen function from {1,2,..., 12} to {A, B, C,..., X, Y, Z} is one-to-one?
Transcribed Image Text:Q1. In the following, explain using the multiplicative principle. You do not need to explicitly evaluate expressions involving factorials, exponents, or fractions. (i) How many functions are there from {1,2,..., 12} to {A, B, C, ..., X, Y, Z}? (ii) What is the probability that a randomly chosen function from {1,2,..., 12} to {A, B, C,..., X, Y, Z} is one-to-one?
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