Question

1. A box contains 20 different balls numbered from 1 to 20 (different balls have different numbers). At each step, we select a ball uniformly at random, record the number on it, and put it back in the box. This experiment is repeated 10 times. Find the probability that all the numbers recorded were distinct.

   (2010)2010

   (2010)⋅10!2010

   10202010

   10102010

   None of the above.

2. We select four distinct integers from the set {1,2,…,20}, uniformly at random (all quadruples of distinct integers are equally likely), and arrange them in ascending order. Find the probability that after ordering them, the second number is equal to 7.

Answer 1