SOLUTION: Question is: On National Public Radio, the Weekend Edition program on Sunday, September 7, 1991, posed the following probability problem: Given a certain number of balls, of wh

Question 950234: Question is:
On National Public Radio, the Weekend Edition program on Sunday, September 7, 1991, posed the following probability problem: Given a certain number of balls, of which some are blue, pick 5 at random. The probability that all 5 are blue is 1/2. Determine the original number of balls and decide how many were blue.
Please show work. Thank you.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let's call the number of blue balls and the number of black balls .
The probability of choosing the first blue ball would then be,

Similarly for the second through the fifth,

So then the probability of getting all 5 is,

That seems pretty daunting, let's take a guess and you'll see that it's not really.
Let's assume , then the equation becomes,

Is that the only answer?
How about , then the equation becomes,

Now it becomes more daunting.

This equation doesn't have an integer solution.
So there's one solution but I'm not sure it's unique.

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