Enumeration exercise ( box with balls of different colors )

Question

I have an enmuration exercie , a box with 4 yellow balls , 8 green ones , 3 red ones and 2 white ones , they asked to calculate the number of cases where we have at least a red ball , ( we take 3 balls out of the box and we have to take them successively without putting them back ) , I started first by the complementary method , so number of cases in general minus cases where was have no red balls ) which gives 17A4 - 14A4 , but I'm not sure if I should multiply 17A4 by perumutation since we pick successively and I don't know if the order matter , please help me

Answer 1

# of ways to get 1 red ball when randomly picking 3 is     3C1•14C2 = 3(91)

# ways to get 2 red balls is 3C2•14C1 = 3(14)

# ways to get 2 red balls is 3C3 = 1

 

Compute these three numbers & sum them.