Counting and Probability Selected AMC 10 Practice Problems

[AMC 12B] A red ball and a green ball are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin  is  for  What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?

[AMC 12A] How many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two? 

[AMC 12A] 

Frieda the frog begins a sequence of hops on a  grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she “wraps around” and jumps to the opposite edge. For example if Frieda begins in the center square and makes two hops “up”, the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops?

[AMC 10] How many ways are there to place  indistinguishable red chips,  indistinguishable blue chips, and  indistinguishable green chips in the squares of a  grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally?