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Probability : Combinations and Random Selection

How many variations in first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners?

In a Chinese restaurant, the menu lists 8 items in Column A and 6 items in column B. To order a dinner, the diner is told to select 3 items from column A and 2 from column B. How many dinners are possible?

Suppose a family plans 6 children, and the probability that a particular child is a girl is 1/2. Find the probability that the 6 child family has exactly 2 girls.

Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probability that both cards are aces.

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