A basket contains five apples, five peaches, and four pears. You randomly select and eat three pieces of fruit. The first piece of fruit is an apple and the next two pieces are peaches. Find the probability of this occurring.

Total number of fruit = 5 + 5 + 4 = 14

P (A) = Probability of picking an apple on first pick = 5/14

P (B) = Probability of picking a peach on second pick = 5/13

P (C) = Probability of picking a peach on third pick = 4/12

All we have to do is multiply these probabilities:

5/14 * 5/13 * 4/12 = 25/546