Combinatorics

[JohnC999]

"An office manager must choose a five-digit lock code for the office door. First and last digits must be odd and no repetition is allowed. How many lock codes are possible?"

The book states there are 5-8-7-6-4 combinations allowed for a total of 6,720 total possible combinations.

My question is, shouldn't it be: 5-7-6-5-4?
- 5 in digit 1 since its 1,3,5,7,9
- 7 in digit 2 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1 and 5
- 6 in digit 3 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1,2, and 5
- 5 in digit 4 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1,2, 3 and 5
- 4 in digit 5 since its 1,3,5,7,9 but can't repeat digit 1

Thanks.

[jnelson0612]

"An office manager must choose a five-digit lock code for the office door. First and last digits must be odd and no repetition is allowed. How many lock codes are possible?"

The book states there are 5-8-7-6-4 combinations allowed for a total of 6,720 total possible combinations.

My question is, shouldn't it be: 5-7-6-5-4?
- 5 in digit 1 since its 1,3,5,7,9
- 7 in digit 2 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1 and 5
- 6 in digit 3 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1,2, and 5
- 5 in digit 4 since its 1,2,3,4,5,6,7,8,9 but can't repeat digit 1,2, 3 and 5
- 4 in digit 5 since its 1,3,5,7,9 but can't repeat digit 1

Thanks.

The only thing that you are forgetting is that zero is a possibility for digit 2, 3, and 4. :-)

[RonPurewal]

in the future, please read and follow the forum rules.

• every thread should contain the complete question as originally presented, with all answer choices.

• the title of the thread should contain the first few words of the problem.

thanks.