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

Question

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

WoundedTiger · Accepted Answer

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

EgmatQuantExpert · Answer

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

King407 · Answer

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

schazamhuzzah · Answer

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

Answer= (2/10c5) ::A

1991sehwag · Answer

10/10 * 4/9 * 3/8 * 2/7 * 1/6 = 1/126

Option A is the answer

shallow9323 · Answer

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

ShashankDave · Answer

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.

Fdambro294 · Answer

1st: Each of the 5 White Marbles are Identical. Each of the 5 Black Marbles are Identical.

However, since Each Girl and Each Boy is Distinct, it matters which Boy or Girl receives a Black or White Marble.

Probability = (No. of Favorable Ways in which the 5 Girls receive B-B-B-B-B or W-W-W-W-W-) / (Total No. of Ways to Distribute the 5 White and 5 Black Marbles among the 5 Girls and 5 Boys)

there are only 2 Favorable Outcomes ------> All 5 Girls receive the 5 Black -OR- All 5 Girls receive the 5 White

_____________________________________________________________
DEN = Total No. of Ways to Distribute 5 Identical Whites and 5 Identical Blacks to -------> 5 Distinct Girls and 5 Distinct Boys

Case 1: All 5 Girls receive 5 White Marbles AND All 5 Boys receive 5 Black Marbles

"5 choose 5" * "5 choose 5" = 1 Way under this Scenario

Case 2: 
4 Girls gets 4 White -AND- 1 Girl gets 1 Black
____________________________________

We need to find all the different ways we can put together a Combination of 4 Girls to give the 4 Whites to. Once we give the 4 Whites away to the 4 Girls, the 5th Girl who gest the 1 Black will automatically be chosen.

we can do this in -----> "5 choose 4" No. of Ways = 5! / (4!)(1!) = 5 Ways
 
----AND----

1 Boys gets 1 White -AND- 4 Boys get 4 Black
_______________________________________

We need to shuffle around the 5 Different Ways for the Girls with all the Different ways we can pair off 4 Boys to give the 4 Black to. Again, once we chose 4 Boys for a given Combination, the 5th Boy who will receive the 1 White will automatically be chosen.

We can do this in: "5 choose 4" No. of Ways -----> 5 Ways

Case 2: 5 * 5 = 25 Different Ways to Distribute the marbles in this Scenario

Case 3: 
3 Girls get White -AND- 2 Girls get Black
___________________________________

Following the Same Logic, how many different ways can we group together 3 Girls to give the White to? Once we have chosen 3 Girls for any given Combination, the 2 Girls who receive the 2 Black will automatically be chosen.

we can do this in: "5 choose 3" No. of Ways -------> 5! / (3!)(2!) = 10 Different Ways

-AND-

2 Boys get 2 White -AND- 3 Boys get 3 Black
_______________________________________

for Each of the 10 Different Ways above, we can shuffle them around with the Number of Different Ways we can give 2 Whites to 2 Boys and 3 Black to 3 Boys. Each of the "shuffles" (i.e., arrangements) will constitute a Unique Distribution of the Marbles

once we choose which 2 Boys will receive 2 White, the 3 Boys who will get Black automatically get chosen.

we can do this in: "5 choose 2" No. of Ways = 5! / (2!)(3!) = 10 ways

Total No. of Unique Distributions under Scenario 3 =
10 * 10 = 100 Ways

Case 4, Case 5, and Case 6 follow the Same Logic as above. However, we just switch around the Black and White.

Case 4: 
2 Girls get 2 White -AND- 3 Girls get 3 Black

---AND---

3 Boys get 3 White -AND- 2 Boys get 2 Black

100 Ways

Case 5:

25 Ways

Case 6:
1 Way in which the Girls receive NO Whites (5 Black)
and
1 Way in which the Boys receive 5 Whites (NO Black)
1*1 =

1 Ways

All the Different Ways to Distribute = DEN = Sum of All 6 Cases =

1 + 25 + 100 + 100 + 25 + 1 = 252

Probability = (2/252) = 1/126

-A-

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

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

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