Can you compute the chances that at least one number does not come up, using derangements?
If we roll a die 20 times what are the chances that all numbers 1 through 6 come up?
I thought the size of the space was 6^20 and then the size of the event would be
(6!*6^12) however this is obviously wrong.
Thanks for any help
Ah ok so If it as all the ways you can choose the 20 with all 6 die thrown then that is the number of surjections from the set of 6 elements to the set of 20 elements which is
.
We then simply divide by the total space 6^20 and arrive at what you have there.
Sorry quite simple I was just thinking of it in a completely and much less helpful way.
thanks a lot (sorry for so much editing I made loads of typo's)