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