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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 5E
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Please do the following questions with handwritten working out from both images
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}.)
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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