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InvisibleLanaM
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So you think you know your math huh...
    #1455338 - 04/13/03 09:10 PM (14 years, 6 months ago)

I'm out with some friends over the weekend and we get into a discussion about numbers. One of my friends brings up a class she had in high school, trig 101.

Anywho, she's trying to tell me that there are only so many combinations of putting 4 digits. In other words, she tried telling me that if you were to use the numbers 0 thru 9 in a four digit sequence, and the numbers can come up as many times as possbile, you'd only have a few (under 10,000 combinations)???

How wrong is that !!!

I tried telling her that if you have 0 - 9 and they can come up over and over again, you'd have millions of combinations. For example, 1234 or 2255 or 9999

My point is, I want to prove this girl wrong! If I can she's owes me dinner.

Isn't there a formula that can tell you how many combinations there are in a sequence of numbers based on the number of digits there are? If so let me know cause my mouth is watering for a good steak dinner!

Thanks,
Lana


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OfflinetrendalM
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Re: So you think you know your math huh... [Re: Lana]
    #1455572 - 04/14/03 06:54 PM (14 years, 6 months ago)

Yes the formula is:

b^n

where b is the base system you are using (decimal is 10, binary 2, octal 8, ect) and n is the number of places you have.

So for a four digit number in decimal, you have:

10^4 = 10000


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OfflineToxicManM
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Re: So you think you know your math huh... [Re: Lana]
    #1455584 - 04/14/03 06:59 PM (14 years, 6 months ago)

Shouldn't the number of combinations be equal to the number of combinations for the first digit times the number for the second times the third times the fourth? Since there are 10 possible values for each digit, the total number of combinations should be 10x10x10x10 = 10,000. It's equivalent in this case to asking how many numbers there are from 0000 to 9999, which is exactly 10,000.

If you're not allowed to have a duplicate digit in the number, then the total is 10x9x8x7 = 5040 possible combinations.

Or the question is something else from either of those.


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OfflinetrendalM
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Re: So you think you know your math huh... [Re: ToxicMan]
    #1455708 - 04/13/03 11:57 PM (14 years, 6 months ago)

Shouldn't the number of combinations be equal to the number of combinations for the first digit times the number for the second times the third times the fourth?

That's the same thing as the formula i posted  :smirk:

10x10x10x10 = 10^4


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OfflineAnnoA
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Re: So you think you know your math huh... [Re: Lana]
    #1456112 - 04/14/03 03:34 AM (14 years, 6 months ago)

You gave yourself the answer already in your question, the highest combination is 9999 and the lowest 0000 and all the combinations inbetween, so all in all 10,000 combinations


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OfflineJackal
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Re: So you think you know your math huh... [Re: Lana]
    #1456171 - 04/14/03 04:11 AM (14 years, 6 months ago)

I think you're thinking of the number of sequences of 4 numbers between 1 and 1000.

e.g.

1 - 65 - 743 - 998

or

321 - 555 - 601 - 677

In this case the number of possible combinations =
(1000*999*998*997)/(1*2*3*4) =
(994010994000)/(24) =
41,417,124,750


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OfflineExtravagantDream
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Re: So you think you know your math huh... [Re: Jackal]
    #1456272 - 04/14/03 04:59 AM (14 years, 6 months ago)

the number of sequences of 4 numbers between 1 and 1000 would be just 24. The numbers 998 or 65 is the whole number and cannont be split. So they would have to stay as (998)(65). They cannon be thrown together such as 96958.

It would be the number of 4 digit sequences.. or something like that. I know what you ment to say, but it can be interpreted differently.


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InvisibleLanaM
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Re: So you think you know your math huh... [Re: ExtravagantDream]
    #1456555 - 04/14/03 09:08 AM (14 years, 6 months ago)

AH CRAP!!! Its 10,000!

Now I owe my friend dinner! Thats the last time I get into a conversaton at 1:00 a.m. after drinking greyhounds all night!

Thanks guys... I appreciate your help.

Lana


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OfflinetrendalM
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Re: So you think you know your math huh... [Re: Lana]
    #1456723 - 04/14/03 11:48 AM (14 years, 6 months ago)

lol  :smirk:


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Offlineneuro
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Re: So you think you know your math huh... [Re: Lana]
    #1460286 - 04/15/03 02:36 PM (14 years, 6 months ago)

You either want to do a nCr or an nPr equation.

nPr =
n!/([n-r]!)

where n is the total number of items (in your case 10) and r is how many you're taking at a time but nothing can be repeated

and nCr =
n!/[r!*(n-r)!]

where n = 10 and r = 4



Edited by neuro (04/15/03 02:46 PM)


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Invisibledjfrog
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Re: So you think you know your math huh... [Re: neuro]
    #1462812 - 04/16/03 03:27 AM (14 years, 6 months ago)

23.40?


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OfflineAnnoA
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Re: So you think you know your math huh... [Re: neuro]
    #1463132 - 04/16/03 08:43 AM (14 years, 6 months ago)

nPr = n!/([n-r]!) ) = 10! / (10-4)! = 5040

nCr = n!/[r!*(n-r)!] = 10! / [4! (10-4)!] = 210

So these are your solutions ??!
Hmmmmm nope, won?t be right....


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Invisiblematts
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[Re: Anno]
    #1463203 - 04/16/03 10:04 AM (14 years, 6 months ago)



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OfflineAnnoA
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Re: So you think you know your math huh... [Re: matts]
    #1463219 - 04/16/03 10:22 AM (14 years, 6 months ago)

>because nothing can be repeated:

Says who?


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Offlineneuro
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Re: So you think you know your math huh... [Re: Anno]
    #1463234 - 04/16/03 10:35 AM (14 years, 6 months ago)

those are the solutions if nothing can be repeated...

the easier way to figure it out, allow for numbers to be repeated, in the case 0001 three 0's would to assign 1 - 1 relationships to the combinations
1) 0000
2) 0001
3) 0002
4) 0003
and so on...
so whatever the last 4 digit number is the counting number assigned to it will the 4 digit number + 1


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Invisiblematts
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[Re: neuro]
    #1463382 - 04/16/03 12:11 PM (14 years, 6 months ago)



Edited by matts (04/16/03 12:21 PM)


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OfflineExtravagantDream
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Re: So you think you know your math huh... [Re: matts]
    #1464167 - 04/16/03 04:57 PM (14 years, 6 months ago)

Absolutely correct.. and dont make me write them out to show it.


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Invisibledjfrog
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Re: So you think you know your math huh... [Re: neuro]
    #1464802 - 04/16/03 07:54 PM (14 years, 6 months ago)

Hah, well, if it were a nail, my hammer would've worked. And I suppose if she were asking for permutations, some fancy factorial moves would have worked.

I still don't think anyone's solution has accounted for 34.68 though. So, still, no ones been right yet.


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OfflinetrendalM
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Re: So you think you know your math huh... [Re: djfrog]
    #1466090 - 04/17/03 03:01 AM (14 years, 6 months ago)

34.68 is the same as 3468 in this case  :smirk:


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OfflineJssMthrFcknChrst
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Re: So you think you know your math huh... [Re: trendal]
    #1466109 - 04/17/03 03:14 AM (14 years, 6 months ago)

Quote:

and dont make me write them out to show it




You shouldn't have said anything.

Count em yourself... :smile:

EDIT: Insert 0000 - 9999 here  :smile:


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Edited by JssMthrFcknChrst (04/24/03 05:43 AM)


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