A box contains 8 pieces each of milk chocolate, white

Question

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

KarishmaB · Answer

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

Zarrolou · Answer

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

nt2010 · Answer

Thanks Karishma for making the probability simple.

The probability of picking 4 dark chocolates is 8/24*7/23*6/22*5/21.

Can you point to a sample question in which the probability would be different in each subsequent pick after the 1st pick?

Suto · Answer

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

KarishmaB · Answer

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...

KarishmaB · Answer

If the first picks have no conditions, all picks are the same.

Suto · Answer

Dear Karishma, Thank you for the explanation. Everything is clear

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A box contains 8 pieces each of milk chocolate, white

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A box contains 8 pieces each of milk chocolate, white

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