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A box contains 8 pieces each of milk chocolate, white [#permalink]

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15 Apr 2013, 07:18

Dear All,

I know this is not a GMAT question but it is very similar. Could someone explain how to answer this question ?

I am with a group of five of my friends. A box contains 8 pieces each of milk chocolate, white chocolate, and dark chocolate. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available pieces. I am the last person to whom the box is passed. Find the chance that I pick 4 dark chocolates.

Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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15 Apr 2013, 09:20

Expert's post

Suto wrote:

Dear All,

I know this is not a GMAT question but it is very similar. Could someone explain how to answer this question ?

I am with a group of five of my friends. A box contains 8 pieces each of milk chocolate, white chocolate, and dark chocolate. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available pieces. I am the last person to whom the box is passed. Find the chance that I pick 4 dark chocolates.

Thank you very much in advance.

Warm regards,

Olivier

Ok, let me give you some ideas. Perhaps you will be able to figure it out.

It doesn't matter whether I am the last person or the first. Since each person is an equal element, the probability that any one picks 4 dark chocolates is the same. Also the probability of picking 4 dark chocolates in the first pick is same as picking 4 dark chocolates in the last pick.

Now we need to find the probability of picking 4 dark chocolates in the first pick.

Find the total number of ways in which you can pick 4 chocolates: all 4 same type, 3 same type 1 different, 2 same 2 same, 2 same 2 different _________________

Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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15 Apr 2013, 09:36

Hi VeritasPrepKarishma,

I read your article, it is very clear! But I wanna know if I have understood correctly Because, as you said, "the probability of picking 4 dark chocolates in the first pick is same as picking 4 dark chocolates in the last pick" the answer should be \(\frac{8}{24}*\frac{7}{23}*\frac{6}{22}*\frac{5}{21}\)

Is it right? Thanks _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: A box contains 8 pieces each of milk chocolate, white [#permalink]

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16 Apr 2013, 03:59

Expert's post

Suto wrote:

Thank you taking the time to explain everything. Is the answer of 8/24*7/23*6/22*5/21 correct ?

Yes it is. Probability of picking dark chocolate in the first pick = 8/24 Now you have only 7 dark chocolates and 23 total so probability of picking it again = 7/23 and so on... _________________

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