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Bunuel
In how many ways 11 identical marbles be placed in 3 distinct jars such that no jar is empty?

A. 72
B. 54
C. 45
D. 42
E. 36


Are You Up For the Challenge: 700 Level Questions

I have been doing such problems by applying 2 equations.
1) when we can distribute 0- n things to r boxes , no of ways = (n+r-1)C(r-1)
2) when we are not allowed to keep any box empty =(n-1)C(r-1)
Applying the second formula, 10C2 =45.
C is the answer.

It would be appreciated if someone can elaborate those two formulas.
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minustark
Bunuel
In how many ways 11 identical marbles be placed in 3 distinct jars such that no jar is empty?

A. 72
B. 54
C. 45
D. 42
E. 36


Are You Up For the Challenge: 700 Level Questions

I have been doing such problems by applying 2 equations.
1) when we can distribute 0- n things to r boxes , no of ways = (n+r-1)C(r-1)
2) when we are not allowed to keep any box empty =(n-1)C(r-1)
Applying the second formula, 10C2 =45.
C is the answer.

It would be appreciated if someone can elaborate those two formulas.

I've always been using only (n+r-1)C(r-1) but when no box can be left empty, I put one marble in each box and apply the same formula for what is left.

So in this case I put one marble in each jar so I'm left with 8 and so n=8, r=3, (n+r-1)C(r-1) = 10C2=45

Posted from my mobile device
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minustark
Bunuel
In how many ways 11 identical marbles be placed in 3 distinct jars such that no jar is empty?

A. 72
B. 54
C. 45
D. 42
E. 36


Are You Up For the Challenge: 700 Level Questions

I have been doing such problems by applying 2 equations.
1) when we can distribute 0- n things to r boxes , no of ways = (n+r-1)C(r-1)
2) when we are not allowed to keep any box empty =(n-1)C(r-1)
Applying the second formula, 10C2 =45.
C is the answer.

It would be appreciated if someone can elaborate those two formulas.

minustark

Please watch the following video in which I have explained where does this property come from

I hope it help! :)
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