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How many ways can you distribute 10 candies among 5 kids, if each kid must get at least one candy?

 Dec 6, 2019

Best Answer 

 #10
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Since each kid must get "at least one candy each", we therefore have them distributed in this manner:

 

[10 - 1] C [5 - 1] =9 C 4 =126 ways.

 Dec 6, 2019
 #1
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Distribute one candy to each kids first.

 

5 candies are left, and I can distribute to them in any configuration.

 

I have 55 = 3125 ways to do so.

 Dec 6, 2019
 #2
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Is that on purpose?

Guest Dec 6, 2019
 #3
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Please explain. I do not understand what you have just said.

MaxWong  Dec 6, 2019
 #4
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what you did

Guest Dec 6, 2019
 #6
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Oh, yes. Considering only the cases that satisfy the condition is quite troublesome, so I want to make sure that each kid gets one candy at the very beginning, so there will be less constraints to consider.

MaxWong  Dec 6, 2019
 #10
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+1
Best Answer

Since each kid must get "at least one candy each", we therefore have them distributed in this manner:

 

[10 - 1] C [5 - 1] =9 C 4 =126 ways.

Guest Dec 6, 2019
 #5
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anyway, how's calc going for you?

 Dec 6, 2019
 #7
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anything interesting?

 Dec 6, 2019
 #8
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I have not been online for quite a while, and I have seldom logged on this site, so I don't know what's happening here.

 

There are not much difference since I last logged on.

MaxWong  Dec 6, 2019
 #9
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What about your studies?

Guest Dec 6, 2019

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