Marbles Combinations problem Martin’s bag of marbles contains two red, three blue and five green marbles. If     he reaches in to pick some without looking, how many different selections might he make?
I do not know how to approach this question. It asks if he were to pick some marbles. What does that mean?
 A: Think first of the number of marbles he can grab.
Case of 0 marbles: 1 case
Case of 1 marble: 3 cases(assuming identical colors are indistinguishable)
Case of 2 marbles: 6 cases(red;red, red;blue, etc)
Case of 3 marbles: Same + 2_of_a_color + 1_of_each_color = 2 + 6 + 1 = 9
Case of 4 marbles: Same + 3_of_a_color + 2_of_2_colors + 2_then_1_then_1 = 1 + 2 + 3 + 3 = 9
Case of 5 marbles: Same + 4_of_a_color + 3_then_2 + 3_then_1_then_1 + 2_then_2_then_1 = 1 + 2 + 4 + 2 + 3 = 12
Now these cases, you basically choose which ones are left out. You would choose how many red, blue, green, etc, etc.
I realize this might be quite tedious, but it's simple, and shouldn't be too difficult. Can you do the last few cases?
A: Martin has $3$ choices for how many red. For he can choose $0$ or $1$ or $2$. For each of these choices, he has $4$ choices for how many blue, and then  $\dots$.
Remark: We assumed that marbles of the same colour are indistinguishable. We also assumed that the choice of no marbles is allowed. That is a matter of interpretation, since one could argue about the meaning of the word "some."
