+0  
 
0
74
2
avatar+262 

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 .

Darkside  Sep 4, 2018
 #1
avatar+2758 
+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.

Rom  Sep 4, 2018
 #2
avatar+91027 
+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

CPhill  Sep 4, 2018
edited by CPhill  Sep 4, 2018

8 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.