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Dec 28 2022 09:26 PM- Currently:
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- Member Title:
- «≡larch bucket≡»
- Age:
- 34 years old
- Birthday:
- January 31, 1991
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Male
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Number of ways to divide identical items into different containers:
= C(items + containers - 1, containers - 1)
= (items + containers - 1)! / (containers - 1)! * (items)!
where order of the items does not matter, as they are identical, but the containers are fixed and their orders matter.
This method is thought of by constructing a string with one space for each item, plus one space for each "divider character." There are (containers - 1) divider characters.
For example, to divide ten balls into two cups, the string model of the first possibility would be "|BBBBBBBBBB" where "|" is a divider. The next possibility would be "B|BBBBBBBBB" and so on. By the formula, this would be C(10+2-1, 1) = (11!/1!*10!) = 11 possible ways to divide.
= C(items + containers - 1, containers - 1)
= (items + containers - 1)! / (containers - 1)! * (items)!
where order of the items does not matter, as they are identical, but the containers are fixed and their orders matter.
This method is thought of by constructing a string with one space for each item, plus one space for each "divider character." There are (containers - 1) divider characters.
For example, to divide ten balls into two cups, the string model of the first possibility would be "|BBBBBBBBBB" where "|" is a divider. The next possibility would be "B|BBBBBBBBB" and so on. By the formula, this would be C(10+2-1, 1) = (11!/1!*10!) = 11 possible ways to divide.
Need a dispenser here.
Comments
Lachesis
21 Jul 2011 - 17:52Lachesis
19 Jul 2011 - 00:20Lachesis
22 Jun 2011 - 00:51Lachesis
21 Jun 2011 - 21:16CJA
13 Jun 2011 - 14:30Lachesis
08 Jun 2011 - 03:54Lachesis
08 Jun 2011 - 03:54Lachesis
08 Jun 2011 - 03:54CJA
05 Jun 2011 - 19:16Lachesis
04 Jun 2011 - 19:24Lachesis
25 Dec 2010 - 03:14CJA
23 Dec 2010 - 22:56Lachesis
23 Dec 2010 - 22:22Lachesis
26 Nov 2010 - 01:38nooodl
17 Jan 2010 - 10:34