# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #26 2011-05-29 21:08:12

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

Yea so my logic is that the first card will always be 100% correct, the next card has a probability of 36/51, and the third will be 22/50, but the fourth has to be the compliment so 42/49. Does that make sense?

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## #27 2011-05-29 21:17:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

No, hold on one second. You have not given all the rules. What is a 3 card badugi?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #28 2011-05-29 21:20:50

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

Ok so basically you are dealt 4 cards, out of the 4 cards, 3 of them have different suits and different values but the last one is either the same suit/value as one of the three. What are the odds of this?
I think you misread the question before.

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## #29 2011-05-29 21:24:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

What about a 3 card badugi. Are you saying it does not matter if some of them are badugis?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #30 2011-05-29 21:25:56

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

There is never a 3 card badugi, for a badugi you need 4 cards with 4 different suits and values.

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## #31 2011-05-29 21:30:12

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

In other words, you are one card away from a Badugi. This is fairly tricky, so be careful with the counting here. The correct answer is between 55% and 60%.

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## #32 2011-05-29 21:31:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

Okay, I will work on it and post when I have something.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #33 2011-05-29 22:01:00

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

Hahaha I knew I was right about the balls and slots, I was just mixing up the variables

Where n is the number of letters and k is the number of slots. We learned the right side of the equation in class so I am more accustomed to that, I just have to figure out which variable is which.

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## #34 2011-05-29 23:08:37

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hi all,

Let me check whether I understood it correct.

First, I'll calculate the number of ways to get a badugi:

52*38*24*10 ways
Do we agree?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #35 2011-05-29 23:25:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

Hi gAr;

That is a little off.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #36 2011-05-29 23:28:30

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hmmm, what went wrong?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #37 2011-05-29 23:31:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

Hi;

It is very difficult to do it that way. I always seem to leave someone out. The right answer I think is 52 * 36 * 22 * 10 another way
is

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #38 2011-05-29 23:43:57

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hi,

I don't understand.
First card can be any: 52
Second card the different suit, and different value: 52 - 13 -1 = 38
Third : 52 - 26 - 2 = 24
Fourth : 52 - 39 - 3 = 10

Something wrong here?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #39 2011-05-29 23:50:05

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

Hi gAr!

Its actually
second card: different sut different VALUE so 52 - 13 - 3 = 36
third card: 52-26 - 4 = 22

Last edited by careless25 (2011-05-29 23:51:35)

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## #40 2011-05-29 23:54:10

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

AHHH!! HAHAHA Bobbym i am pretty sure that is not the right answer....remember the hint: it is between 55% and 60%...ur answer is 6.3%

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## #41 2011-05-29 23:55:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #42 2011-05-29 23:58:55

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

Oh! I thot

Nvm that is actually correct and agrees with my answer for the probability of getting a badugi.

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## #43 2011-05-30 00:01:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

Yes, that is for a badugi. I was just showing a simpler way for gAr.

How do you know the 3 card problem is 55% - 60%?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #44 2011-05-30 00:12:34

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

That was stated in the question. (I did not post it when i posted the question)

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## #45 2011-05-30 01:20:49

careless25
Real Member
Registered: 2008-07-24
Posts: 560

### Re: Perms and Combs! and some induction..

3 cases:
1. diff value, same suit as one card

2. diff suit, same value as one card

3. same suit, same value with another card

make sense???

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## #46 2011-05-30 01:24:54

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hi all,

The answer I get is :
52*36*24*39 / (52*51*50*49)

I get the same by direct counting also.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #47 2011-05-30 01:54:02

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hi,

We can consider only 2 cases:
1)
Fourth card is of one of the suites already there:
52*36*24* (36)

2)
Fourth card is of the other remaining suit:
52*36*24* (3)

Hence 1) + 2) = 52*36*24* (36+3) ways

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #48 2011-05-30 05:11:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

Hi;

That is what I got but he said it was between 55% and 60% which I do not yet understand.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #49 2011-05-30 05:20:11

gAr
Member
Registered: 2011-01-09
Posts: 3,482

### Re: Perms and Combs! and some induction..

Hi bobbym,

Since computer too verifies it, I guess 55-60% must be a mistake, or the question is incomplete.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #50 2011-05-30 05:31:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Perms and Combs! and some induction..

That is what I was thinking.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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