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Temurkhon
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How many ways to arrange the 8 balls ?

8!/3!3!2! = 540 > Permutation eliminating duplicate colors

How many ways to arrange the balls where a red is in the third position ?

Arrange remaining 7 balls

7!/3!3! = 140

Probability 140/560 = 1/4

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  1. All the balls except one red ball: 7/8
  2. Since 1 ball is selected we are left with: 6/7
  3. Last is to select 1 Red ball amongst 2 Red balls (since we don't know which was selected in "7/8") : 2/6

7/8*6/7*2/6 =1/4

ans: 25%
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This is how I solved it. There could be 3 type of cases of getting red in 3rd pick when picking 3 balls without replacement.

Case 1:
Not Red _ Not Red _ Red
6/8 * 5/7 * 2/6 = 5/28

Case 2:
Red _ Not Red _ Red
2/8 * 6/7 * 1/6 = 1/28

Case 3
Not Red _ Red _ Red
6/8 * 2/7 * 1/6 = 1/28

Adding Case 1,2,3
5/28 + 1/28 + 1/28 = 7/28 = 1/4 or 0.25

Thus, answer is option A (0.25).
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Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

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