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how many ways are there to divide 5 indistinguishable candies among 3 distinguishable friends

note that all candies must be distributed , and people can recieve 0 candies

   

please give a detailed solution .

 Sep 4, 2018
 #1
avatar+4436 
+1

I'm not going to answer this one as you need to start doing your own work but I will tell you how to look at it to solve it.

 

Put the 5 candies down on a table.

 

Use 2 straws to divide them up into 3 groups.

 

Now figure out how many different ways you can place the straws.

 Sep 4, 2018
 #2
avatar+98128 
+1

5 0 0     =  3 ways   -  any of the 5 candies can  be given to one person

 

4 1 0  =   6 ways  = one candy can be given to any one person (3 ways) and the other 4 can be given to one of the other two (2 ways)  ...so...3 x 2  =  6

 

3 2 0  =   6 ways -  any of the three candies can br given to one person (3 ways)  and the other two can be given to one of the other two (2 ways)...so....3 x  2  = 6

 

3 1 1  =   3 ways    -  any of the 3 candies can be given to any one person (3 ways) ...since the other two candies are indistinguishable...we can distribute them to the other two people in any manner

 

2 2 1   =   3 ways  -  any 1 of the candies can be given to any of the three people....the other 4 can be split equally between the remaining two people

 

So...  3 + 6 + 6 + 3 + 3  = 21 ways

 

 

cool cool cool

 Sep 4, 2018
edited by CPhill  Sep 4, 2018

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