1. ## combinations and permutations

i'm sorry if i'm in the wrong area. i need to know how many possible combinations there can be of a pair of trainers where, for example, each part has a different number of colours to choose from.

as follows

Part 1: 12 colours
Part 2: 24 colours
Part 3: 24 etc
Part 4: 36
Part 5: 4
Part 6: 9
Part 7: 48
Part 8: 24
Part 9: 36
Part 10: 11
Part 11: 12
Part 12: 4
Part 13: 4
Part 14: 11
Part 15: 37

can you direct me to the right place to ask this question if i'm in the wrong place?

thanks

barny

p.s. i'm not a mathematician, this is really because i want to know the answer and trainers are really what i am interested in..

2. I have absolutely no idea what that question could possibly mean.

Please try again. More details. A good example.

3. ## sorry

ok i'm sorry. here we go.

so let's say that you can design your own pair of trainers. on a specific pair, there are 15 parts to the trainer to personalize. each part has a number of colours to choose from.

a simple example is that there are 2 parts, back and front, and two colors for each part, black and white. the possible combinations for the trainer as a whole would be 4 i think... i.e. white and white, black and black, blacj and hite and white and black.

my problem is harder because there are 15 parts to the trainer but each part has a different number of colours to choose from. this is what my table represents... the order doesn't matter.

what i want to find out is how many possible variants of the whole shoe there could be. i know this will be an astronomical number.

i have repeated the table below because that is the true example. part 1 has 12 colours to choose from, part 2 has 24 colours to choose from and so on.

thanks again for you help

Part 1: 12
Part 2: 24
Part 3: 24
Part 4: 36
Part 5: 4
Part 6: 9
Part 7: 48
Part 8: 24
Part 9: 36
Part 10: 11
Part 11: 12
Part 12: 4
Part 13: 4
Part 14: 11
Part 15: 37

4. There are a several ‘ifs’ to this answer.
If each trainer has 15 parts and if each color is unique then the number of possible combinations of trainers is simply the product of all the possible numbers of colors.

But say a trainer has only three parts: 1, 4, & 10.
Then the number of possible trainers of this type is $(12)(36)(11)= 4752$

Is that even close to what you mean?

5. ok well we can say that yes, the trainer has all 15 parts. this is standard.

the colours aren't necessarilt unique. the 12 colours available to choose from for part 1 are also available in the other parts, the other parts though, sometimes have extra colours.

also, say there were 2 parts and each part had 12 of the same colours to choose from then it wouldn't just be 12 X 12 would it?

surely it would be more like 12 ^ 12?

6. basically, how many different trainers can be made?

if i designed a pair i could leave every part white. or i could colour one part black and leave the rest white. or i could colour one part white, one part black, one part orange, one part blue, and leave the rest white etc etc.

whatever i did, i would have one pair of trainers out of a possible how many pairs that could be made?

sorry, i am not good at explaining stuff like this...

7. ## multiplication rule

If all those parts of the "trainer" are independent, you just multiply all the numbers together. For instance:

I am getting dressed for work tomorrow.
I have at my disposal:
2 pairs of shoes
3 pairs of socks
4 pairs of underwear
5 pairs of pants
5 shirts
3 ties

How many possible outfits do I have that I could wear tomorrow?

$2\cdot 3 \cdot 4 \cdot 5 \cdot 5 \cdot 3 = 1800$

So in your case get on a computer/calculator and start multiplying. hint: it is a lot and my calculator won't do it I don't think.

8. I just did it on google and here is what it told me. There are
$3.19339054 \times 10^{17}$ unique trainers possible.

That is $319,339,054,000,000,000$ in case you don't know scientific notation.

three hundred nineteen quadrillion, three hundred thirty nine trillion, fifty four billion

Now, a question for you. What the heck is a trainer?

9. thanks for all of your help.

a trainer is a shoe - like a sneaker i guess. the type i'm concerned with is adidas because they have a thing where you can design your own trainer. they provide the template and you can choose different materials and colours for the different sections. i wanted to know how many different possibilities of design there could be on one model of trainer.

just one quick point... a friend of mine argued that the equation should be more like this.. can you clarify that they are wrong and the calculation as above is in fact correct?

by the way - the full number is - 319,339,053,654,736,896

it should be:

Part 1: 12
Part 2: 24
Part 3: 24
Part 4: 36
Part 5: 4
Part 6: 9
Part 7: 48
Part 8: 24
Part 9: 36
Part 10: 11
Part 11: 12
Part 12: 4
Part 13: 4
Part 14: 11
Part 15: 37

= 12! + 24! + 24! + 36! + 4! + 9! + 48! + 24! + 36! + 11! + 12! + 4! + 4! + 11! + 37!
=(12*11*10*9*8*7*6*5*4*3*2*1) + (24*23*22*21*20*19*18*17*16*15*14*13 etc etc)

I think, but I am afraid Maths A Level was many years ago.....
Hope that this helps x

10. This thread is perfect example why I hardly ever attempt to answer such questions?
Mathematicians and other folks just don’t speak the same language.

If I were to build a custom training shoe, had to choose colors for each of fifteen parts of the shoe, and each part has the number of possible colors listed in your post then there would be $12\cdot 24\cdot 24\cdot 36\cdot 4\cdot 9\cdot 48\cdot 24\cdot 36\cdot 11\cdot \cdot 12\cdot 4\cdot 4\cdot 11 \cdot 37=319339053654736900$
possible ways to build that shoe.

11. ## thanks

guys thank you very much. it has taken me months to find this answer out, i have bored friends and work colleagues, i even got in touch with adidas. sorry if my explanations weren't so clear but i think we got there in the end and i'm very happy to have a confirmed answer.

thanks again

barny

12. Originally Posted by Plato
This thread is perfect example why I hardly ever attempt to answer such questions?
Mathematicians and other folks just don’t speak the same language.
I was sure you were going to say "mathematicians and normal folks"!

If I were to build a custom training shoe, had to choose colors for each of fifteen parts of the shoe, and each part has the number of possible colors listed in your post then there would be $12\cdot 24\cdot 24\cdot 36\cdot 4\cdot 9\cdot 48\cdot 24\cdot 36\cdot 11\cdot \cdot 12\cdot 4\cdot 4\cdot 11 \cdot 37=319339053654736900$
possible ways to build that shoe.
Don't you read Harry Potter? They are forever referring to their "trainers"- It is the British term for what we would call "sneakers". I remember a few years ago there was a rage in the U.S. for "cross-trainers" which essentially meant a show that could be used in a variety of sports. Whether the British term is from that or predate it I don't know.

But you know the British! I remember being shocked when reading about how Sherlock Holmes "knocked up" Mrs. Hudson! And don't get me started on "Spotted Dick".

15 different parts that may be 15 different colors? Gaudy! Can we at least assume that both shoes are the same colors? In that case, Plato is right: multiply all the numbers together.

Fundamental Principle of Counting: If A can happen (or be chosen) in m ways and B can happen in n ways, then A and B can happen in mn ways.

13. well you'll all be pleased to know that i ordered my trainers today. i left them totally white, 100% un-designed, except i wrote the number of possible combinations as text across the heel. the problem i had was that 319 quadrillion was too many digits for one trainer/sneaker. so i ordered 2 - one had the first eight digits, the second had the second eight digits and when they arrive i will swap them around so both pairs display the correct number.

this may sound geeky but i got obsessed.

again, thanks for everyone's help

catch you later

barny