Carcass wrote:
Each of the four children has a bag with five different colored discs in it; red blue green yellow and orange. If each child in succession randomly chooses exactly one disc from his bag to flip into a hat. What is the probability that hat will no hold no repeated colours at the end flipping?
A- 1/5
B- 6/625
C- 24/625
D- 24/125
E- 6/125
As with most probability questions on the GRE, we can use either counting techniques or probability rules.
Let's use
probability rules:
P(no repeated colors) = P(ANY color disc is chosen 1st
AND color of 2nd disc is different from 1st disc
AND color of 3rd disc is different from 1st and 2nd disc
AND color of 4th disc is different from other discs)
= P(ANY color disc is chosen 1st)
x P(color of 2nd disc is different from 1st disc)
x P(color of 3rd disc is different from 1st and 2nd disc)
x P(color of 4th disc is different from other discs)
= 1
x 4/5
x 3/5
x 2/5
= 24/125
Answer: D