Hi, I have the following problem which I don't know how to solve:

"A fair die is thrown 20 times. Find the probability that all of the six numbers appear at least once."

I think the number of possible combinations is 6^20, but I don't know how to work out the numerator... I know 14.7 is the average number of times that the die needs to be thrown so that all sides appear at least once (1+6/5+6/4+6/3+6/2+6/1=147/10=14.7), but I don't know if I have to use this, and if I do, I don't know how . Thanks a lot for your help!