Problem
12 points An bag contains 5 pink balls, 7 purple balls, and 4 white balls. Three balls are selected, one after the other, without replacement. Find the probability that all three balls are purple.
Solution
Step 1 ：\(\frac{7}{16}\times\frac{6}{15}\times\frac{5}{14}\)
Step 2 ：\(\frac{7!}{3!4!}\times\frac{15!}{12!3!}\times\frac{14!}{11!3!}\)
Step 3 ：\(\frac{35}{286}\)
