Answer
288
Work Step by Step
"Alternatives" imply the addition principle
"Sequence of steps" implies the multiplication principle
---------------------------
four red marbles,
two green ones,
one transparent one,
three yellow ones
two orange ones.
(total = 12 marbles)
----------------------------
There are 3 yellow and 9 non-yellow marbles in the bag.
At least 2 yellow = (exactly 2 yellow) OR (exactly 3 yellow)
Alternative 1: 2 yellow, 3 non-yellow
STEP 1: select 2 of the 3 yellows ... C(3,2)=3
STEP 2: select 3 of the 9 non-yellows ... C(9,3)=84
(total 1 = 3(84)=252)
Alternative 2: 3 yellow, 2 non-yellow
STEP 1: select 3 of the 3 yellows ... C(3,3)=1
STEP 2: select 2 of the 9 non-yellows ... C(9,2)=36
(total 2 = 1(36)=36)
TOTAL = 252+36=288