There are x black balls, (x-2) yellow balls, and (x+2) green balls in a bag. The probability of choosing 2 black balls when 2 balls are picked at random is 1/12. Find the total balls in the bag.

Correct answer: 9

Solution

C(x,2)/C(3x,2) = 1/12. x(x-1)/[3x(3x-1)] = 1/12. (x-1)/[3(3x-1)] = 1/12. 12(x-1) = 3(3x-1). 12x-12 = 9x-3. 3x=9. x=3. Total = 3×3 = 9.

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