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Chapter 10: Problem 64

Solve by the method of your choice. How many different four-letter passwords can be formed from the letters \(A, B, C, D, E, F,\) and \(G\) if no repetition of letters is allowed?

Short Answer

Expert verified
So, there are 840 different four-letter passwords that can be formed from the letters \(A, B, C, D, E, F, and G\), when no repetition of letters is allowed.

Step by step solution

01

Compute options for the first letter

There are 7 possible choices for the first letter of the password, as we have not used any of the 7 letters yet.
02

Compute options for the second letter

Once a letter has been chosen for the first letter, there are only 6 letters left to choose from for the second letter.
03

Compute options for the third letter

After choosing the first two letters, 5 choices will remain for the third letter.
04

Compute options for the fourth letter

After the first three letters have been chosen, only 4 remains as the choice for the 4th letter.
05

Calculate the total possible combinations

The total number of possible four-letter passwords comes to the product of the number of choices for each letter, because each letter is chosen independently of the others. Using the principle of multiplication in counting, it will be \(7 * 6 * 5 * 4\) = \(840\)

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