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**+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**+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

CPhill
Sep 4, 2018