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A password is 4 characters long and must consist of 3 letters and one number. If letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400.

Sagot :

Mwhite0602idn

Answer: 156,000 is the right answer.

Step-by-step explanation:

Using the Fundamental Counting Theorem, it is found that 156,000 possibilities are there, and option c is correct.

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]

In this problem:

  • The password starts with 3 characters, that cannot be repeated, hence [tex]n_1 = 26, n_2 = 25, n_3 = 24[/tex].
  • It ends with a digit, hence [tex]n_4 = 10[/tex].

Thus, the number of possibilities is given by:

N = 26 x 25 x 24 x 10 = 156,000.

To learn more about the Fundamental Counting Theorem, you can check https://brainly.com/question/24314866

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