Answer
a) $\frac{1}{7880400}$
b) $\frac{1}{8000000}$
Work Step by Step
a) The probability that Abby takes the first place is 1/200.
After Abby, the probability that Barry is second is 1/199. As the 1st place is already taken by Abby.
The probability that Sylvia takes the third place is 1/198. As the 1st and 2nd places are already occupied.
Hence the Probability that Abby, Barry, and Sylvia win
the first, second, and third prizes, respectively is $1/200 \times 1/199 \times 1/198 $ =$\frac{1}{7880400}$
b)If one person is allowed more than one prize then the probability of 2nd and third changes to 1/200 for both.
Hence the Probability that Abby, Barry, and Sylvia win
the first, second, and third prizes, respectively is $1/200 \times 1/200 \times 1/200 $ =$\frac{1}{8000000}$