A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
A. Start Fraction 10 over 27 End Fraction
B. Start Fraction 5 over 91 End Fraction
C. Start Fraction 5 over 98 End Fraction
D. Start Fraction 93 over 182 End Fraction
Once Jack picks a peach, there are now 3 apples, 2 oranges, 2 bananas, 2 pears, and 4 peaches left in the basket. Bethany now has 1 orange out of 16 remaining fruits. Therefore, the probability of Jack getting a peach and Bethany getting an orange is:
$P(\text{Jack gets peach and Bethany gets orange}) = \frac{5}{12} \times \frac{2}{16} = \frac{5}{96}$
So the answer is $\boxed{\textbf{(C) } \frac{5}{98}}.$