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# in how many ways can an employer distribute 100 one rupee notes among 6 employees so that each gets atleast one note

Posted on 2014-12-05
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in how many ways can an employer distribute 100 one rupee notes among 6 employees so that each gets atleast one note

i have tried as follows but i am not able to understand the solution

This is the number of  positive solution of x1+x2....+x6=100
so the required numer is C(100-1,100-6)=71523144
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Question by:shivangi bhatnaagr
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LVL 27

Accepted Solution

d-glitch earned 250 total points
First you give one note to each employee.
Now you have 94 notes that you can divide up among the six employees without restriction.

Take your 94 notes:     RRRRRRRRRRRRR . . . . R
and 5 dividers:              | | | | |

This a total of 99 items.

The number of ways to arrange them is       99!/(94!*5!)
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LVL 84

Assisted Solution

ozo earned 250 total points
It's the same as giving each employee one rupee, and then distributing the remaining 100-6 notes among 6 employees
Imagine lining up 94 one rupee notes in a row, with 5 dividers placed somewhere among them,
Then each of of the 6 employees can get the notes between 2 dividers, or the notes at the beginning or end
The number of ways to line up 94 notes and 5  dividers is (94+5)! / 94! / 5!
or C(99,94)
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Author Comment

nice explaination
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LVL 27

Expert Comment

Hello shivangib,

And welcome to Experts Exchange.  I see this is your first day and first question.

It is great when you get the same answer from two experts so quickly.
You might want to consider splitting the points in this situation.
That makes things more collaborative and less competitive, which can be essential with more difficult problems.

If you hit the Request Attention above the first comment, you will be able to do this.
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