WTF is happening????? I did sign in. how come it is showing me as a guest???? I know i am a member of this board!!

Help me moderator (or somebody)

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- 08-20-2002Jet_Master
WTF is happening????? I did sign in. how come it is showing me as a guest???? I know i am a member of this board!!

Help me moderator (or somebody) - 08-20-2002Eibro
You have to use the user cp if you want to sign in (well most people do...)

Quote:

According to your wording, all five people own all five hats, so the probability is 1 in 1.

- 08-20-2002moonwalkerAsk the master if it's math
First, let's see ...

Probability = (Favourable Outcomes) / (Total Number of outcomes)

Favourable Outcomes....

it's when all the five have their own

hats... no other combination is acceptable... so only 1 favourable

outcome

Total Outcomes ....

Five hats can be given to 5 people in 5! ways

5! = 5 * 4 * 3 * 2 * 1 = 120

Probability (P) = 1/120

Have fun :) - 08-20-2002moonwalkerand....
now you ask me

**why**5! ways ?

observe the pattern carefully... if you can follow

till 3, you'll understand...

1 person ... 1 hat ... 1 way ... ( 1! )

2 persons .. 2 hats ... 2 ways ... ( 2! )

3 persons ... 3 hats ... 6 ways ... ( 3! )

4 persons ... 4 hats ... 24 ways ... ( 4! )

5 persons ... 5 hats ... 120 ways .... ( 5! )

from the above pattern,

n persons ... n hats ... n! ways - 08-20-2002moonwalkeranother explanation...
here's another way of looking at it (if you're still interested)

5 hats - 1 2 3 4 5

5 girls :D - A B C D E

probability of A getting the right hat (out of 5 hats)

1/5

probability of B getting the right hat (out of remaining 4 hats)

1/4

probability of C getting the right hat (out of remaining 3 hats)

1/3

probability of D getting the right hat (out of remaining 2 hats)

1/2

probability of E getting the right hat (out of remaining 1 hat)

1/1

Now if A gets the right hat, no one else gets A hat (sounds

dumb, but see...) ... it's the same for B C D & E

so these "events" tell us that it is conditional probability.

so, the probability of everybody getting their own hats is

1/5 * 1/4 * 1/3 * 1/2 * 1/1 = 1/5!

someone here said 1/3125

that answer will be correct if the person "picks" the right hat

and puts it back again ... and the rest do the same ("pick" the

right hat and put it back again)

Math is fun :) - 08-20-2002Cshot
1/5! = 1/120

Simple stats question. - 08-20-2002DISGUISEDQuote:

1/5 * 1/4 * 1/3 * 1/2 * 1/1 = 1/5!

- 08-20-2002BMJ
:D

Odds of contracting and being affected by the West Nile virus in Illinois: 1/30000 - 08-20-2002DISGUISEDQuote:

*Originally posted by BMJ*

**:D**

Odds of contracting and being affected by the West Nile virus in Illinois: 1/30000

- 08-20-2002BMJ
meh? Oh... yea, heh; Lucky :)

I just saw a bunch of stats, so I just felt like posting something :p - 08-20-2002DISGUISED
I am just glad I live downtown..I don't see to many bugs here.

- 08-21-2002MrWizard
Okay , early i said 1/120 , I am sticking with that answer. Here is a little reasoning. Lets assume you have 5 objects. There are only a certain number of permuations for this set. 2 Permuations are

1,2,3,4,5

1,2,3,5,4

Just for example. To get the total number of permuations you do 5! which equals 120. Only 1 of those is right however because each of the 5 owners only owns 1 hat. So 1/120 is the correct answer. It doesn't matter if you pass out the hats all at once OR one by one, the answer holds. - 08-21-2002Troll_King
Is it a permutations answer or a combinations answer? I don't want to think about, but my guess after reading was 5! or 1 in 120 that each individual would recieve their own hat.

- 08-21-2002moonwalkerhmm
probabilities are usually based on permutations.

combinations come into place when it doesn't matter

which way you give the hat as long as they get hats..

Eg.

The number of combinations of 3 girls :D sitting together in

3 seats is 1.

(doesn't care about arrangements.. as long as they sit

together, it's a combination.. different ways of arrangements

of the same are considered as repitition)

The number of permutations of 3 girls sitting together

in 3 seats is 6.

(does care about arrangements)

Now why would we want to study combinations then?

It's when we want to cancel out repititions.

For example, the number of ways of "choosing" 3 girls

from 12 girls is 12 C 3 (doesnt matter which way you

choose the girls, as long as you choose 3 of them)

The number of ways of "arranging" 3 specific girls out

of 12 is 12 P 3 (it matters which spice girl you pulled out

1st, 2nd and 3rd ;) ) - 08-21-2002Unregistered
Most of you put what was expected: 1/25.

But the correct answer is: 1/120.

Thanks Again