+0  
 
0
10
1
avatar+4 

Seven distinct pieces of candy are to be distributed among three bags. The red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. How many arrangements are possible?

 

so first I put one candy in each of the red and blue bags, which was \(7\cdot6\) choices. now we only have 5 candies left to sort so that is \(3^5\) possibilities (because for each remaining candy, they have 3 options for which bag to go into).

 

and in all, that would be \(7\cdot6\cdot3^5=10206\) which is wrong

 

help

 Oct 23, 2023
 #1
avatar+118617 
0

You have double counted.

ex:

If candy A,B,C go into the blue bag that is the same as    B,C,A going in the blue bag.

 

If I have time I will look more later    :)

 Oct 25, 2023

2 Online Users

avatar