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#1 2006-12-21 17:47:19

balasvce
Member
Registered: 2006-12-20
Posts: 37

justification plzz

38) seven one dollar bills are to be distributed among Lucia,

Gomel, & Doming so that each person receives at least $1.

col a
the number of ways to distribute the bills so that at least

one person receives at least $3

col b
the total number of way to distribute the bills


ans given is c (both column a & b are equal) justify !!!

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#2 2006-12-22 01:27:55

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: justification plzz

since everyone at least gets 1 dollar , the total way to distribute the money is 3x3x3x3=81 . when  each of them gets 2 dollars  there is one dollar left , that means there will always be a people who has 3 dollars or more .so the number of ways of cola is equal to the total ways Then there are 81 ways to distribute the money.


Numbers are the essence of the Universe

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#3 2006-12-22 03:06:14

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: justification plzz

Your answer is a bit too high. For example, if the first 4 dollars went to one person and the other 3 dollars went to the second person, then you're counting that as a different outcome as if the first 3 dollars went to the second person and the other 4 dollars went to the first.

Given that everyone has to get 1 dollar, it's really only 4 dollars that get distributed, because the first 3 are always fixed. I believe that the total number of combinations of distributing those 4 dollars among the 3 people is 15.


Why did the vector cross the road?
It wanted to be normal.

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#4 2006-12-22 03:18:14

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: justification plzz

Going with Mathsyperson's idea, there are 12 ways to distribution the additional 4 dollars.  It can be divided $4, $0, $0 (3 different ways to do that), $3, $1, $0 (6 different ways to do that) or $2, $2, $0 (3 different ways). 

D    G    L
5     1    1
1     5    1
1     1    5
4     2    1
4     1    2
2     4    1
2     1    4
1     4    2
1     2    4
3     3    1
3     1    3
1     3    3

And someone is always going to get at least $3 so that requirement is also met.

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#5 2006-12-22 03:59:49

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: justification plzz

There's also $2, $1, $1, and there are 3 ways of doing that as well.
In the table, it would be:

D  G  L
3   2  2
2   3  2
2   2  3


Why did the vector cross the road?
It wanted to be normal.

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#6 2006-12-22 04:28:35

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: justification plzz

You're right Mathsyperson!   Good catch.

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#7 2006-12-22 04:33:45

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: justification plzz

yeah , you are right mathsyperson


Numbers are the essence of the Universe

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