NUMBER PROPERTIES GUIDE PROBABILITY

[calebjli]

Example in chapter 3: 5 digit lock first and last must be odd and no repetition

I don't think they do it right
They have 5x8x7x6x4

To make it simpler lets say it's 3 digits
Then:
5x5(if second is even)x4+5x4(if second is odd)x3

There's no repetition and the answer doesn't consider if the middle numbers are odd that eliminates choices for the fifth number. Am I missing something? Also 0 is even and should be total of ten choices.

[RonPurewal]

Example in chapter 3: 5 digit lock first and last must be odd and no repetition

...

I don't think they do it right

They do it right.

They have 5x8x7x6x4

The two pink things -- the things that are restricted -- are chosen first.
We're not picking the digits from left to right. We're picking them first, then last, then the other three.

To make it simpler lets say it's 3 digits
Then:
5x5(if second is even)x4+5x4(if second is odd)x3

Sure, you can do that, but it's not efficient.

If you pick the first and last digits (the ones that are restricted to odd numbers) first, then there are 5 and 4 options, respectively, for those choices.
Then you've used 2 digits, so there are 8 digits left over for the middle.
So, 5 x 8 x 4 = 160.

If you multiply out what you have here (5x5x4 + 5x4x3), you'll find that it's also 160. But more work.

[RonPurewal]

There's no repetition and the answer doesn't consider if the middle numbers are odd that eliminates choices for the fifth number.

Please try to put punctuation in your sentences. The way it is now, this is very hard to read.

If we pick the first and last digits before we pick the middle digits, then there's no need to consider whether the middle digits are even or odd. Once the first and last digits have been picked, the whole even/odd issue stops being a thing.

Don't feel compelled to pick things from left to right if it doesn't make sense to do so.

Also 0 is even and should be total of ten choices.

Yes, and that's why the middle three choices are 8, 7, 6 after you've already picked 2 digits (the first and last ones).

[calebjli]

I got it.
I was using my iPhone to type.

[jnelson0612]

Great!

[barlemon942]

I really enjoy this theme you've got on in your web page. What is the name of the template by the way? I was thinking of using this style for the site .

[tim]

I'm not sure any of us have any information about this that isn't available publicly.