AbhiJ wrote:There is an assumption in this problem that all the same colored marbles are identical. If they are different then the answer would be 2/(!10)

abhisays wrote:The answer is A

Here comes the solution ::

probability = no. of favorable cases/ total no. of cases.

the total number of cases will be (10*9*8*7*6*5*4*3*2*1) = 10!

logic is... first ball can be selected in 10 ways second in 9 and so on.

favorable no. of cases = 5!5! + 5!5! = 2*5!5!

logic is.. here only same color of marble will go to girls..

so the answer will be 2*5!5!/10!

siebecker wrote:I thought the likelihood of 5 girls picking the same colored marbles was pretty slim to start. After looking at the answer choices I thought it highly unlikely that choices C D or E were correct. That left A and B. I then did 10*9*8*7*6/5*4*3*2*1. That gave me 252. Since that wasn't one of the choices I divided it by 2 figuring 5 was half of 10 and low and behold it's 126. 1/126 was a choice. Bingo. Not so pretty but at this point in my studying, that's how I'd have done it on the exam.

Himanshu Vyas wrote:I also got "A"..Here is the simplest approach:

Prob = Favorable/Total

Now, Total i.e. Choosing 10 marbles out of 10 without replacement(meaning Permutation)=10P10 =10!
And, Favorable i.e. {(5 girls choose 5 whites without replacement) AND( 5 boys choose 5 blacks without replacement )} OR {(five girls choose 5 blacks without replacement)AND (five boys choose 5 whites without replacement)} = 5P5 x 5P5 + 5P5 x 5P5 = 2x (5P5x 5P5)= 2x5!x5! (Analogy--> AND is "x" , OR is "+")

Therefore, Prob = 2x5!x5!/10! = 1/126 (Ans)

Hi BRENT: Please let me know your feedback on this approach!!

edge wrote: Doesn't the order of selection change the conditional probabilities? Do the boys go first? Do the boys and girls take turns picking their marbles?