BMAT 2010 · Question 23 · Ratio/Proportion/Percentage
SaveOne fund-raising activity of a particular sports club is a weekly draw. Participants choose two different numbers between 1 and 15 inclusive. When the draw is made, two numbers between 1 and 15 inclusive are selected at random. The prize money is shared by anyone who has chosen these two numbers. If there are no winners, the prize fund rolls over to the following week. When last week's winning numbers were announced as 3 and 10, someone pointed out that it was the fifth successive week that the two numbers consisted of a total of three digits, all different.
What is the probability that when two different numbers between 1 and 15 inclusive are selected at random they will consist of three digits all different?