Problem Solving

you can do either way 1st girl then boy then girl then boy so on
or

1st boy 2nd girl 3r boy 4th girn so on Probablity will remail same

1 * 5/9 * 4/8 * 4/7 * 3/6 * 3/5 * 2/4 * 2/3 * 1/2 * 1 = 1/126

Answer: A)

Explanation:

We have 10 Marbles (5W and 5B) and we have 10 Individuals (5 girls and 5 boys)
1) The first girl steps out and picks a marble. So the probability here of this girl picking any colored marble is 1.
2) The second girl steps up and picks the same colored marble as the previous girl, in this case, say assume that the first girl picked a White colored marble. Hence, the probability of the 2nd girl picking the same color is: 4/9 =
3) Similarly, third girl steps up and the probability of her picking a white marble is: 3/8 and so on...

So the probability that all five girls pick the same colored marble would look something like this = 1 x 4/9 x 3/8 x 2/7 x 1/6 = 1/126

Please find the solution in the attachment

Answer is A. Quite Easy. 5 White, 5 Black and 5 Boys 5 girls. 5 white marbles can be distributed among 5 girls in 5! ways and 5 Black among 5 Boys in 5 ! ways. so total ways of distributing=5! * 5!. Same for vice versa( black to girls and white to boys). There fore favorable outcomes=2*5!*5!. Total ways of distributing 10 marbles among 10 persons = 10!. Therefore (2*5!*5!)/10!=1/126

(1/4)*(1/9)*(1/7)*2=1/126

apologies for junk post. posted a doubt but found my mistake

Another way we can compute it

2 (white or black)*5!(5 white/Black arranged among 5 girls)*5!(White/Black arranged among 5 boys)/10!

Brent@GMATPrepNow wrote:The answer is, indeed, A (1/126)
Here's my solution:
The easiest/fastest way to determine the probability is to examine the probability of each necessary outcome to guarantee that the girls (and subsequently the boys) draw the same colored marble.
We get [P(1st girl selects any marble) x P(2nd girl selects marble the same color as 1st girl) x P(3nd girl selects marble the same color as 1st girl) x P(4th girl selects marble the same color as 1st girl) x P(5th girl selects marble the same color as 1st girl) x P(boys getting same color ball from remaining balls)
This equals: 1 x 4/9 x 3/8 x 2/7 x 1/6 x 1
Which equals: 1/126

Girls can draw only black or white marbles, therefore possible in 2 outcomes

The total number of outcomes is 10!
But since we have only 2 different elements it should be divided by 5! 5! (10!/5!(10-5)!)

10! / (5! 5!) = 252

so the answer is

2/252 = 1/126 (A)

Thanks for giving the ans in prob of girls picking 5 same coloured marbles.
1X 4/9 X 3/8 X 2/7 X 1/6= 1/126

An alternative solution with the same answer:

There are exactly
2 ways the girls can have 5 the same (e.g. 00000 or 11111) = 2
10 ways the girls can have exactly 4 the same x 5 remaining combinations for boys = 50
20 ways ways the girls can have exactly 3 the same x 10 remaining combinations for boys = 200
Which gives a total of 252

2/252 = 1/126

What about these permutations WBBBBBWWWW or WWBBBBBWWW or likewise..... in these cases as well 5 girls (assuming they are choosing black) will get the same color.

neerajkumar1_1 wrote:I thought of it in a different way...
essentially the answer will be the same...

There will be two required combinations...

WWWWWBBBBB or BBBBBWWWWW

i suppose the key is that one should realize that the prob of boys picking up the ball is 1...

so prob = 5/10 * 4/9 * 3/8 * 2/7 * 1/6 * 2

= 1/126
Pick A

I had answer B because I did:

1/5*1/4*1/3*1/2*1/1 = 1/120

So if I understand, my mistake is to choose a color a the first step ?

Brent@GMATPrepNow wrote: To better understand/identify your mistake, I need to know what each part represents.

To begin, what does the 1/5 stand for?

Cheers,
Brent

It's the probability to have a white or black marble.
And then, 1/4 is the probability to have the second marble with the same color, and so on.

Here is my logic, Considering the girls part of the question.

Number of ways they can select a ball of same color is 2.

Total Number of ways 5 girl can select a ball each from the 10 balls available is 10C5.

So probability = 2/ 10C5 (10C5 = 10!/5!5! = 252) ==> 2/ 252 == > 1/126

Hence my answer is A.