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Each of the four children has a bag with 5 different colored discs in

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Each of the four children has a bag with 5 different colored discs in  [#permalink]

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New post Updated on: 08 Aug 2015, 06:27
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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

Either OA given by 800score is wrong or my understanding is wrong. Cos my answer is D.
EDIT---OA edited as per Gmat Insight Answer.

Originally posted by sahil7389 on 08 Aug 2015, 04:31.
Last edited by sahil7389 on 08 Aug 2015, 06:27, edited 1 time in total.
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Re: Each of the four children has a bag with 5 different colored discs in  [#permalink]

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New post 08 Aug 2015, 06:01
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sahil7389 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 hold no repeated colours at the end of the flipping?


A- 1/5
B- 6/625
C- 24/625
D- 24/125
E- 6/125

Either OA given by 800score is wrong or my understanding is wrong. Cos my answer is D.


ALTERNATE:

The first child can choose any disc out of 5 so probability of him choosing a disc of different color = 5/5 = 1

The Second child can choose any disc out of remaining 4 Colours so probability of him choosing a disc of different colour = 4/5

The Third child can choose any disc out of remaining 3 Colours so probability of him choosing a disc of different colour = 3/5

The Forth child can choose any disc out of remaining 2 Colours so probability of him choosing a disc of different colour = 2/5

Finanl Probability of all the events to happen simultaneously = (5/5)*(4/5)*(3/5)*(2/5) = 24/125

Answer: option D
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Re: Each of the four children has a bag with 5 different colored discs in  [#permalink]

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New post Updated on: 08 Aug 2015, 06:01
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sahil7389 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

Either OA given by 800score is wrong or my understanding is wrong. Cos my answer is D.


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

Answer: option D
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Originally posted by GMATinsight on 08 Aug 2015, 05:48.
Last edited by GMATinsight on 08 Aug 2015, 06:01, edited 1 time in total.
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Re: Each of the four children has a bag with 5 different colored discs in  [#permalink]

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New post 26 Jun 2017, 12:53
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sahil7389 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 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:

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Re: Each of the four children has a bag with 5 different colored discs in  [#permalink]

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