20 replies to this topic

[Nick]

Okay, so say there are numbers 1-36 on a key bad.
Your job is to guess the 3-digit access code, and each number can be used only once in the 3-digit sequence.

However, the order does matter! So, while 1, 22, 18 would work - 1, 18, 22 would not.
Catch my drift?

Now, I'm wondering, first, how many possible combinations there are taking the order of the numbers as a factor.
Second, say the order didn't matter and you could put 1 2 3 or 3 1 2 and both would work - how many possible combinations are there now.

Thanks in advance for help guys!

[rcadble]

Answers:
If order matters: 46,656 combinations
If order doesn't matter: 42,840 combinations

Solving It:
If order matters: 36^3

If order doesn't matter: 36 nPr 3 (permutations, from 36 choose 3).
The formula for this is

You can calculate nPr on a TI calculator though. Anyways, this may or may not be correct, I haven't done probability since 7th grade.

[Just Another User]

Answers:
If order matters: 46,656 combinations
If order doesn't matter: 42,840 combinations

That can't possibly be right, if order matters there should be a lot less combinations...

You were right for non-ordered, ordered uses this formula:

CODE

     n!          36!
---------- = ---------- = 7140
r!(n - r)!      3!33!

Edited by Just Another User, 21 August 2008 - 07:53 AM.

[Vitalis]

That can't possibly be right, if order matters there should be a lot less combinations...

You were right for non-ordered, ordered uses this formula:

CODE

     n!          36!
---------- = ---------- = 7140
r!(n - r)!      3!33!

That formula is for Combinations, isn't it? In Combinations, the order doesn't matter. Since in the first scenario, order does matter, you would have to use the formula for Permutations, which is nPk = n!/(n-k)!

I'm not sure what I'm doing anymore.

Edited by Vitalis, 21 August 2008 - 08:06 AM.

[Reaper]

I don't know anything about math, I actually really suck...I would have just figured that there would be more possibilities...hmmm..I suppose I should have listened in "dumb" math more.

[Just Another User]

That formula is for Combinations, isn't it? In Combinations, the order doesn't matter. If order does matter, you would have to use the formula for Permutations, which is NPr = N!/(N-r)!

I'm probably wrong though. Probability and me don't really hang.

Oh yea... i got it the wrong way around, i guess rcad is wrong on both things then

combinations: well google says 6.8852459 × 10^37
permutations: 42840

meh... google is shit, i need my calculator but i can't find it...

Edited by Just Another User, 21 August 2008 - 08:13 AM.

[rcadble]

Haha, I don't know what the fuck I was doing last night, the formula for order matters should be 36 * 35 * 34, meaning I got the other one wrong. Oh well.

[Eeyore]

Ewwwwwww statistics D=. *leaves*

[Ives]

Mathematics is beautiful. It's a shame I understand too little of it.

[Just Another User]

Ewwwwwww statistics D=. *leaves*

It's combinatorics, not statistics!

Edited by Just Another User, 22 August 2008 - 07:41 AM.

[Just Another User]

Still had to suffer through it in Stats modules though. *Hated*

pfft S1 was an awesome module! I got full marks on that mother bell curve ftw

[Just Another User]

Pfft, I was all about C2. Although D1 was blatantly the easiest, they basically gave you 100% if you turned up.

C2 was god awful, i can't even remember what it was, just that it was really bad although C3 was possibly worse... damn identities

My school didn't even offer D, i had to do stats and mechanics

[Just Another User]

C2 was eaaaaasy, it was something like 70% really basic differentiation and integration. <3 I quit Maths at Xmas of A2 though, was doing too many subjects. Couldn't have done Stats because everybody did S1 in AS and I took it a year early and chose to do Decision. It was such a doss module.

Ah... integration... that was a nightmare, and then they took it even further in C4! Does that mean you finished maths early, or you only did it to AS?

[Just Another User]

Only did it to AS. Then had a year of not really doing any Math, picked it back up in A2 but dropped it after a term because I was doing too many other subjects.

Ah right that's cool, so you're one of those that took like 10 a-levels then?

[Eeyore]

Still had to suffer through it in Stats modules though. *Hated*

This.

Even at degree level, it comes under statistics D=.

[Vegas]

What majors did u guys take? All these complicated sounding math words makes me wanna cry