yahtzee problem! due in 9 hours!

the problem is the following:

In the game of Yahtzee (or Yacht), five dice are thrown. Show that the probability of throwing a large straight (5 numbers in a row, the order does not matter) is 5/162 .

Alternatively, you may solve the following, harder, problem. Show that the probability of throwing a small straight (4 numbers in a row) is 10/81 . Do not count small straights which are also large straights.

so i did the first part as follows :

the 5 numbers in a row can be wether 65432 or 54321 thus the chances to get them will be : 2(5*4*3*2*1)/6^5 but i don't really know how to represent my answer in a professional way !! for the second one, i got no clue how to do it !!

ps: we throuw the dices only once not like in the real game when we throw them twice (i think).

thank you for your very needed help