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The Castroville High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so

The Castroville High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were 12 total bottles. 7 of the bottles contained purple soap. If a club member randomly selects 8 bottles to pour into the first soap bucket, what is the probability that exactly 5 of the chosen bottles contain purple soap? Write your answer as a decimal rounded to four decimal places

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