In a weekly lottery, ten ping-pong balls numbered 0 to 9 are placed in each of six containers, and one ping-pong ball is drawn from each container. To win the prize, a participant must correctly identify the ping-pong ball that is drawn from each of the six containers. If Juan played the lottery last week and didn’t win, what is the probability that he will win this week?

He will have a 1/531,441 chance of winning next week.

There are 10 balls in each container; for 6 containers, this gives us 10^6 = 1,000,000.  There is 1 correct combination of balls, so his chance the first week is 1/1,000,000.

The second week, 1 ball is removed from each container; this will give us 9^6 = 531,441 chances.  There is 1 correct combination, so he will have a 1/531,441 chance of winning.