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How many ways are there to put 3 one dollar bills and 10 quarters into 4 boxes?

2007-01-29 04:03:12 · 3 answers · asked by burritohat 1 in Science & Mathematics Mathematics

Each box is unique.

2007-01-29 04:11:42 · update #1

3 answers

Assuming, the ways to place the dollars are not dependent on the ways to place the quarters and the dollars and quarters are identical, and the boxes are not..
There are 4 ways to put all dollars in one box.
There are 4 x 3 ways to put two dollars in one box and one dollar in the remaining three boxes.
There are 4 x 3 x 2 ways to put one dollar in three boxes.

By the same token, there are 4 ways to put all the quarters in one box, (10/0/0/0)
4 x 3 (9/1/0/0)
4 x 3 x 2 (8/1/1/0)
4 x 3 x 2 x 1 (7/1/1/1)
4 x 3 x 2 x 1 (6/2/1/1)
4 x 3 x 2 x 1 (5/2/2/1)
4 x 3 x 2 x 1 (4/2/2/2)
4 x 3 x 2 x 1 (3/3/2/2)
4 x 3 (8/2/0/0)
4 x 3 x 2 (7/2/1/0)
4 x 3 x 2 x 1 (6/2/1/1)
4 x 3 x 2 x 1 (5/2/2/1)
4 x 3 x 2 x 1 (4/2/2/2)
4 x 3 (7/3/0/0)
4 x 3 x 2 (6/3/1/0)
4 x 3 x 2 (5/3/1/1)
4 x 3 x 2 x 1 (4/3/2/1)
4 x 3 (6/4/0/0)
4 x 3 x 2 (5/4/1/0)
4 x 3 x 2 x 1 (4/4/1/1)
4 x 3 x 2 x 1 (5/5/0/0)


If the dollars are not identical (paper money with serial numbers)
Then the order taken is needed.

Add up all the ways of the dollars and multiply by all the ways of the quarters.

2007-01-29 06:05:49 · answer #1 · answered by a simple man 6 · 0 0

I'm guessing duplicates don't count, like:
1 dollar, 1 dollar, 1 dollar, 10 quarters = 1 dollar, 10 quarters, 1 dollar, 1 dollar

Man, this question is hurting my brain.

2007-01-29 04:16:53 · answer #2 · answered by bequalming 5 · 0 0

Are the boxes identical? For example is placing all the money in the first box a different way than putting all the money in the second box?

2007-01-29 04:11:14 · answer #3 · answered by hayharbr 7 · 0 0

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