Question about deordering
Say you have a bag with 4 red marbles, 7 blue marbles, 8 green marbles, and 8 purple marbles. You pick 4 marbles. If you want to find the ways you can get one of each marble, is it (4choose1)(7choose1)(8choose1)(8choose1) and then do you have to de-order it by multiplying it by 4! because otherwise it is just 4 x 7 x 8 x 8 and that implies a specific order?
arpanshah: March 19, 2015, 10:34 p.m.
If you put the whole thing over 27C4, then I think that will remove the order. So it's just what you have, (4choose1)(7choose1)(8choose1)(8choose1) divided by 27C4
PeterH: March 19, 2015, 11:32 p.m.
You would only divide if it asked what the probability of getting one of each marble was.
arpanshah: March 19, 2015, 11:43 p.m.
Oh, oops, I definitely ready that wrong. I think that you do have to include 4! as a way to de-order it then.
Lilyhui: March 19, 2015, 11:45 p.m.
I would think the answer is fine as it is and do not need to deorder anything
Lilyhui: March 19, 2015, 11:46 p.m.
Not certain the reasoning is correct but I assumed that selecting the green marble will not affect the selection of the other colors. (same for all the other colors)
weisbart: March 20, 2015, 1:41 a.m.
PeterH and Lilyhui have it right. There is no order here because the generations of choices correspond to the identification of the colors, not how the marbles are chosen. There is no first marble chosen, second marble, and so on, there is only the choice of red marble, the choice of blue marble, and so on.