Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

A password is to be made from a string of five characters chosen from the lowercase letters of the alphabet and the numbers 0 through 9.

A Password Is To Be Made From A String Of Five Characters Chosen From The Lowercase Letters Of The Alphabet And The Numbers 0 Through 9 class=

Sagot :

Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:

a) 60,466,176.

b) 5,961,600.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Item a:

No restrictions, hence for each of the five characters, there are 36 outcomes, hence [tex]n_1 = \cdots = n_5 = 36[/tex].

Then, the possible number of passwords is:

[tex]N = 36^5 = 60466176[/tex]

Item b:

The letters and the digits have to be alternated, hence:

  • Starting with a letter, [tex]n_1 = n_3 = n_5 = 36, n_2 = n_4 = 10[/tex].
  • Starting with a digit, [tex]n_1 = n_3 = n_5 = 10, n_2 = n_4 = 36[/tex].

Then, the possible number of passwords is:

[tex]N = 36^3 \times 10^2 + 10^3 \times 36^2 = 5961600[/tex]

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.