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Chapter 11: Problem 19

How many different four-letter passwords can be formed from the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F},\) and \(\mathrm{G}\) if no repetition of letters is allowed?

Short Answer

Expert verified
The total number of different four-letter passwords that can be formed is \( 7 * 6 * 5 * 4 = 840 \)

Step by step solution

01

Different Letter Combination Consideration

First, consider that there are 7 options for the first letter of the password, because none of the letters have been used yet and no repetition is allowed.
02

Further Letter Combination Consideration

Next, realize that once the first letter of the password has been chosen, there are now only 6 remaining unused letters for the second letter in the password. This same logic applies for the remaining two letters, where there will be 5 remaining options for the third letter, and 4 options for the last letter.
03

Calculation of Total Permutations

To find the total amount of possible four-letter passwords, multiply the number of possibilities for each letter together: 7 (possible first letters) * 6 (possible second letters) * 5 (possible third letters) * 4 (possible last letters)

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