There are 9 people taking part in a raffle.
Ann, Bob, Hans, Jim, Kira, Lena, Omar, Ravi, and Soo.
Suppose that prize winners are randomly selected from the 9 people.
Compute the probability of each of the following events.
Event A: Bob is the first prize winner, Lena is second, and Ann is third,
Event B: The first three prize winners are Soo, Omar, and Kira, regardless of order
Write your answers as fractions in simplest form.
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Explanation:

1. Event A: Bob is the first prize winner, Lena is second, and Ann is third,

Thus, the joint probability that Bob is the first prize winner, Lena is second, and Ann is third is the product of the three calculated probabilities:

2. Event B: The first three prize winners are Soo, Omar, and Kira, regardless of order

When the order does not matter, the number of combinations for three different persons win the 3 prizes is C(3,3), which is computed with the corresponding formula:

Thus:

And the number of possible combinations of winners is C(9,3):

Then, the probability is the number of favorable combinations, C(3,3) = 1, divided by the number of possible combinations, C(9,3) = 84:

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step-by-step explanation: