There are 3 blue disks, 5 green disks, and nothing else in a container. Disks will be chosen one at a time, and at random and without replacement, from the container, until all 3 blue disks have been chosen. What is the probability that the third blue disk will be the seventh disk chosen?

Hmm…ok, let me take a shot… Is the answer 1/56?

The way I did is…first, I drew it out… So you basically have 8 disks. 3 blue (B), 5 green(G)… of which 7th one is fixed (that’s my constraint)…which I mean I will work backwards…

So I basically have 7 spots/dashes i.e. _ _ _ _ _ _ _ _, and the seventh one is fixed

_ _ _ _ _ _ B

Since my 7th disk has to be the third blue, it means I have gotten my first two blues before… so basically, my “arrangement” could look like this:

B B G G G G B

Now, whats the probability of each spot?

(3/8) * (2/7) * (5/6) * (4/5) * (3/4) * (2/3) * (1/2)

Now, most numerators and denominators are same and get cancelled out, so I dont do all the math… and I am basically left with 1/ (8*7)= 1/56…

Let me know if this is correct!

As we know that the 7th spot is fix for blue disc , the real question becomes in how many ways we can arrange the remaining 2 blue and 4 green disk (You listed one of the combinations but in this case we have to calculate all the possible one) .

just one more step remain is to calculate all the ways we can arrange those 2 blue and 4 green disk so

6! /(2! x 4!) =15 . So, our final answer becomes 1/56 * 15 or 15/56

It asks for probability of a certain position, right?

So it shouldn’t matter what the arrangement before the 7th is per se. The main thing is that I have 2 blue disks and 4 green disks in every single combination before I get the third blue disk… So the probability of the 6 positions, irrespective of whether it is BBGGGG or GGGGBB or BGBGGG etc, will always result in 1/56 (for the 7th disk to be the third blue disk)…

Unless the question asks in how many different ways can I get the 7th disk to be the blue disk, then the answer would be like you rightly said 15/56…

Actually, now I’m not quite sure… I’ve been treating this as a order doesnt matter question, but it kinda could be that order before matters, so aashiz, you should cross-check once… sorry if i caused any confusion!