Each of the four children has a bag with five different c

[BTGModeratorVI]

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

Answer: D
Source: 800GMAT

[Brent@GMATPrepNow]

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

Answer: D
Source: 800GMAT

As with most probability questions on the GMAT, 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

Cheers,
Brent

[swerve]

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

Answer: D
Source: 800GMAT

Total Outcomes = 5*5*5*5 = 5^4 [Because every child has 5 ways to choose one disc from his/her bag]

Favourable Outcomes = 5C4*4!
[5C4 are the ways to select 4 colours out of 5 colours for discs
and
4! are the ways to arrange the different coloured discs among 4 children]

i.e. Favourable Outcomes = 5C4*4!= 5*24 = 120

Probability = 120/5^4 = 24/125

Therefore, D

[Scott@TargetTestPrep]

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

Answer: D
Source: 800GMAT

The first child can flip a disc of any color into the hat; thus, his probability is 5/5 = 1. The second child can flip a disc of any color other than the color the first child has already flipped; thus, his probability is 4/5. Using the same analogy, the probability of the third child is 3/5 and that of the fourth child is 2/5. Therefore, the overall probability is 1 x 4/5 x 3/5 x 2/5 = 24/125.

Answer: D