Question 8
For some particular website, the password must start with one of the letters , or F . Then there
must be 5 more characters, and each of those characters may be a numeric digit or a letter of the
alphabet. How many different passwords are possible?
There are
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Ask by Blake Stephens. in the United States

Mar 30,2025

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Question 8
For some particular website, the password must start with one of the letters , or F . Then there
must be 5 more characters, and each of those characters may be a numeric digit or a letter of the
alphabet. How many different passwords are possible?
There are
Question Help: Video
Submit Question

Ask by Blake Stephens. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

To find the number of different passwords possible, we need to consider the constraints given:

1. The password must start with one of the letters $$ \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E} $$, or F.
2. There must be 5 more characters after the first letter.
3. Each of the 5 additional characters can be a numeric digit or a letter of the alphabet.

Let's break down the calculation:

1. The first character can be any of the 6 letters (A, B, C, D, E, or F).
2. For each of the 5 additional characters, there are 26 possible letters (A-Z) and 10 possible numeric digits (0-9), making a total of 36 possible characters for each position.

The total number of different passwords possible is the product of the number of possibilities for each character position:

$$ 6 \times 36^5 $$

Now, let's calculate this:
Calculate the value by following steps:
- step0: Calculate:
  $$6\times 36^{5}$$
- step1: Rewrite the expression:
  $$6\times 6^{10}$$
- step2: Calculate:
  $$6^{11}$$
The total number of different passwords possible is $$6^{11}$$ or approximately $$3.627971 \times 10^{8}$$.
There are $$6 \times 36^5$$ different possible passwords, which is approximately $$3.627971 \times 10^{8}$$ passwords.

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