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# A bag contains 5 white marbles and 5 black marbles. If each of 5 girls

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Math Expert
Joined: 02 Sep 2009
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A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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20 Jan 2015, 06:40
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A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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20 Jan 2015, 22:28
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Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

Consider a case when all girls select black marbles...So Girl 1 will chose 1 black marble out of 10..and black marble will be chosen from 5 Black marbles

Girl 1 will have a probability of picking black marble 5/10
Girl 2 will have to pick a black marble out of 4 and total remaining no. of marbles 9=4/9

So we have Probability of all girls selecting black marbles as 5/10*4/9*3/8*2/7*1/6 =1/252

Since Girls can also select white marbles so we will have 2 cases so Probability of girls selecting all same colour marbles is 2*1/252 or 1/126

Ans is A
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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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07 May 2015, 08:23
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Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

First girl can pick any marble, rest of the girls should pick same as her

=> P(First Girl) = $$\frac{10}{10}$$(as she can choose any marble) and rest follows;

=> $$1*\frac{4}{9}*\frac{3}{8}*\frac{2}{7}*\frac{1}{6} = \frac{1}{126}$$

Hence Answer is A
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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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24 May 2015, 03:35
total possibilities: 5 girls can choose any 5 of the 10 marbles => 10c5
Total favourable: all 5 girls choose only white or black = 2 posibilities

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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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24 May 2015, 03:45
10/10 * 4/9 * 3/8 * 2/7 * 1/6 = 1/126

Option A is the answer
Intern
Joined: 16 May 2015
Posts: 14
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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26 May 2015, 06:15
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Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

Please let me know if my logic is correct

I looked at as.
first, total ways to select for all boys and girls,
that is, 10!/(5!*5!)= 252
then there are one two way girls can have all same colors, either white or black.

Therefore, total favorable outcomes/total outcomes = 2/252= 1/126
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Posts: 1222
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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27 May 2015, 01:59
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Expert's post
shallow9323 wrote:
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

Please let me know if my logic is correct

I looked at as.
first, total ways to select for all boys and girls,
that is, 10!/(5!*5!)= 252
then there are one two way girls can have all same colors, either white or black.

Therefore, total favorable outcomes/total outcomes = 2/252= 1/126

Dear shallow9323

Your logic is perfectly correct!

For the benefit of other students reading this thread, this alternate approach is described in detail below:

Total number of ways in which the 5 girls can select 5 balls out of 10 balls = 10C5 = 10!/(5!*5!) = 252
(Note: Once the girls select 5 balls, the remaining 5 balls are automatically selected for boys)

The number of ways in which 5 girls can select 5 white balls = 5C5 = 1 (because there are only 5 white balls and all of them have to be selected)
The number of ways in which 5 girls can select 5 black balls = 5C5 = 1

So, number of favorable cases = (No. of ways to select 5 White balls) + (No. of ways to select 5 black balls) = 1 + 1 = 2

So, probability of Event = 2/252 = 1/126
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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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24 Nov 2016, 21:34
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.

Bunuel
Please help.. to count the number of all possible outcomes..we have used
$$10c5$$
But this is used when all of the objects are distinct..but here there are 5 similar things of one kind and 5 of the other. Please elaborate on this..as this will help me understand a lot.
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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

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11 Feb 2018, 21:23
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Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls   [#permalink] 11 Feb 2018, 21:23
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# A bag contains 5 white marbles and 5 black marbles. If each of 5 girls

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