Question 3 The code for Alice's bicycle lock consists of an 8-digit number sequence wil digits chosen from the set: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and repeated digits allowed. (a) How many possible codes are there? (b) How many codes start with the sequence 987? (c) How many codes end with the sequence 321?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve all parts 3
Question 3
The code for Alice's bicycle lock consists of an 8-digit number sequence with
digits chosen from the set:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
and repeated digits allowed.
(a) How many possible codes are there?
(b) How many codes start with the sequence 987?
(c) How many codes end with the sequence 321?
(d) How many codes start with the sequence 987 or end with 321 (or both 2
(e) The manufacturer of the lock warns the user that it is important to
remember the code because it would be practically impossible to guess
a code. Given that Alice can check any 8-digit sequence in 6 seconds,
estimate the probability that she will find the code within 10 hours if she
has forgotten her code.
In
Transcribed Image Text:Question 3 The code for Alice's bicycle lock consists of an 8-digit number sequence with digits chosen from the set: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, and repeated digits allowed. (a) How many possible codes are there? (b) How many codes start with the sequence 987? (c) How many codes end with the sequence 321? (d) How many codes start with the sequence 987 or end with 321 (or both 2 (e) The manufacturer of the lock warns the user that it is important to remember the code because it would be practically impossible to guess a code. Given that Alice can check any 8-digit sequence in 6 seconds, estimate the probability that she will find the code within 10 hours if she has forgotten her code. In
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