Math Formula Wanted (Page 3): That’s because it yields 6,760,000 possible plates, more than double the population of Utah, not nearly enough for California. Here in Virginia it’s...

SuperflyTNT Loc: Manassas VA

paulrph1 wrote:

Yes is is LNN LNN always in Utah not CA which is a whole issue. Me too with the headache but one must do something with their time. So is it 26x10x10x26x10x10. I give up.

That’s because it yields 6,760,000 possible plates, more than double the population of Utah, not nearly enough for California. Here in Virginia it’s LLL-NNNN which gives us 175,760,000 possibilities.

TreborLow

paulrph1 wrote:

Here is one my imagination deals with and that is the combinations of license plate numbers. letters and numbers combined. X97 B12 with all the numbers available how would you calculate the numbers of possibilities.

Just substitute "26" for each letter and "10" for each numeral and Multiply everything.
26x10x10x26x10x10 = 6,676,000.

Dannj

TreborLow wrote:

Just substitute "26" for each letter and "10" for each numeral and Multiply everything.
26x10x10x26x10x10 = 6,676,000.

That formula would allow for letters and numbers to be repeated, yes?
My head is spinning🥴

Virgil Loc: The Hoosier State

2697 x 2612 = 7,044,564

Virgil Loc: The Hoosier State

ACTUALLY i THINK IT MIGHT BE 2699 X 2699 = 7,284,601 !

lwiley Loc: Los Banos, CA, USA

jerryc41 wrote:

Let's say a product is available with the following choices:

4 shapes
3 body colors
4 trim colors
2 sizes

What formula would tell me how many variations are possible?

Per a google search and reviewing an old Statistics book, the equation for determining the possible number of combinations is : Combinations (C) = n! / (r! X ((n-r)!)). Where n is the number of starting units and r is the number of possible variations and ! means Factorial of number (4*3*2*1). For just the 4 shapes and 3 possible body colors the possible combinations is 4. Remember that the starting is 4 shapes of 2 sizes or 8 possible units that could be painted 3 possible body colors you would need 6720 units. And then add units with each of the 4 trim colors, I hope you have a lotttttttt of room in your house.

TriX Loc: Raleigh, NC

What we really have is 4 objects (n) taken 1 (r) at a time * 3 objects taken 1 at a time * 4 objects taken 1 at a time * 2 objects taken 1 at a time or 4 * 3 * 4 * 2 = 96 which is also intuitively correct. The combination formula is correct for each choice of an attribute, but the total number of choices is the product of each combination.

JBRIII

My wife was very very good at statistics including graduate level courses, but never had a course which covered combinatorites. I used a lot of statistics, but never had any courses, so I signed up for one and dropped it several weeks later. It was nothing this stuff, if you have 4 white flags and 3 red and 2 black, how many combinations if "NO MORE" than 2 can be white, 1 red and 2 black, etc. There are many formulas, but unlike this discussion logic never helped me remember them. Also, in 40 years of doing research, such questions never arose. Statistics is mostly about describing data, averages, etc. or predicting likely results from a smaller data set, i.e., will the vaccine work well or not so well, based on a few hundred people who got the virus from 30,000 in the test set of people.

SuperflyTNT Loc: Manassas VA

Virgil wrote:

ACTUALLY i THINK IT MIGHT BE 2699 X 2699 = 7,284,601 !

And you think wrong.

SuperflyTNT Loc: Manassas VA

Virgil wrote:

2697 x 2612 = 7,044,564

Where are you getting these numbers.

Dannj

lwiley wrote:

Per a google search and reviewing an old Statistic... (show quote)

My brain has a hard time accepting that there could be 6,720 possible combinations using just 4 parameters.
4 shapes in each of 3 colors yields 12. (4 X 3) outcomes.
Allowing for each of those 12 to have 1 of 4 trim colors gives us 48 possibilities. (4 X 12)
Each of those possibilities is available in either of two sizes giving us 96
(2 X 48) in total.
What am I missing?

Dalek Loc: Detroit, Miami, Goffstown

I just want to know if Walmart carries whatever it is!
Ps it is a combination (order does not matter) not a permutation (order matters).

JBRIII

Dannj wrote:

My brain has a hard time accepting that there could be 6,720 possible combinations using just 4 parameters.
4 shapes in each of 3 colors yields 12. (4 X 3) outcomes.
Allowing for each of those 12 to have 1 of 4 trim colors gives us 48 possibilities. (4 X 12)
Each of those possibilities is available in either of two sizes giving us 96
(2 X 48) in total.
What am I missing?

I believe strongly you are correct.
In this case which is picked first is irrelevant. Some of the other formulas assume order is important. Doesn't matter if you pick a car model first, then color, it is the same if picking order is reversed. Other combinations aren't like that. Picking a red flag, then a blue could signal something completely different than the reverse.
That is why combinations totally baffled me, but statistics made sense.

Dannj

JBRIII wrote:

I believe strongly you are correct.
In this case which is picked first is irrelevant. Some of the other formulas assume order is important. Doesn't matter if you pick a car model first, then color, it is the same if picking order is reversed. Other combinations aren't like that. Picking a red flag, then a blue could signal something completely different than the reverse.
That is why combinations totally baffled me, but statistics made sense.

We’re on the same page. If I remember correctly, permutations and combinations fall under the umbrella of probability theory. Statistics are a little more straightforward, if that makes sense. I had a lot of trouble with both in school🥴

TriX Loc: Raleigh, NC

Dannj wrote:

My brain has a hard time accepting that there could be 6,720 possible combinations using just 4 parameters.
4 shapes in each of 3 colors yields 12. (4 X 3) outcomes.
Allowing for each of those 12 to have 1 of 4 trim colors gives us 48 possibilities. (4 X 12)
Each of those possibilities is available in either of two sizes giving us 96
(2 X 48) in total.
What am I missing?

You’re not missing anything. The combination formula is correct, but only when you define the terms correctly. Each time you calculate a combination, you define n ( the number of choices ) and r ( the number from those choices that you choose ), such as I choose 1 (r) of 4 (n) possible choices. The question then becomes how to you combine multiple choices, and that is simple multiplication.

Here’s an example. Let’s assume you have 4 digits, each of which can be anything from 0 to 9. It’s obvious that the answer is 10,000 (0000 to 9,999) possible combinations. For each digit, the n =10, and the r=1, so per the formula, it’s equal to n! / r!(n-r)! or 10! / 1!*9! = 10, and for all 4 digits, it’s equal to 10*10*10*10 or 10,000. It’s NOT 10 choices (n) taken 4 (r) at a time. If it were, the total number would be 10! / 4!*6!, which is obviously not correct.