rxs0005
A deck of cards contain 2 red , 3 blue , 4 green cards. Three cards are drawn
with replacement from the deck. What is the probability that all 3 cards are different colors
2/9
3/20
1/5
2/7
8/243
rxs0005
This is poor quality question, with bad wording and wrong OA.We are looking for the probability of RBG.
If the drawing is WITH replacement (as in the original question) then: \(P(RBG)=3!*\frac{2}{9}*\frac{3}{9}*\frac{4}{9}=\frac{16}{81}\), multiplying by 3! as scenario RBG can happen in 3! # of ways (RBG, RGB, ...);
If the drawing is WITHOUT replacement then \(P(RBG)=3!*\frac{2}{9}*\frac{3}{8}*\frac{4}{7}=\frac{2}{7}\), the same reason of multiplying by 3!.
If the question is posted exactly as it is in the source and the OA is indeed 2/7 then I wouldn't study from this source. Also I suggest not to spend time on studying, posting, answering bad quality questions.