Math Is Fun Forum

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 !!!

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.

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Numbers are the essence of the Universe

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.

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

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.

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

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

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: justification plzz

You're right Mathsyperson!   Good catch.

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: justification plzz

yeah , you are right mathsyperson

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Numbers are the essence of the Universe