A sample of four ball is to be selected at random from an urn containing 16 balls numbered 1 to 16. If seven of the balls are green, four are white, and five are black, how many different samples of four balls contain all three colours?

Question

anonymous · Answer

7 x 4 x 5 x 13

anonymous · Answer

I think

anonymous · Answer

the answer is 910. I don't know how to solve.

anonymous · Answer

ok, so my answer is pretty close, only off by a factor of 2 , so now I have to think why

valpey · Answer

gwbg = 7*4*5*6/2
+gwbw = 7*4*5*3/2
+gwbb = 7*4*5*4/2
=7*4*5*(6+3+4)/2

valpey · Answer

divide by 2 because the order of the two same colored balls doesn't matter