Binomial distribution help please

I need help with these questions PLEASE !

1.Two dice are rolled simultaneously and their difference is recorded. Find the probability that in 5 rolls:
a) a difference of zero occurs at least once
b) a difference of 1 occurs at least twice
c) a difference of 5 occurs at least once

THANKS SO MUCH !!!

N =P

There are 36 combinations in the sample space:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

a) The only way to get a difference = 0 is when the dice are equal to (1,1) (2,2) , ... (6,6). Since there are only 6 possibilities, then P = 6/36 = 1/6. Conversely, the probability is 5/6 that the difference does NOT equal zero.

P(a difference of zero occurs at least once) = 1 - P(none) = 1 - (5/6)^5 = 4651/7776 = 0.5981

b) A difference of 1 can happen 10 ways. P = 10/36 = 5/18

P(at least twice) = P(2) + P(3) + P(4) + P(5) = 1 - P(0) - P(1) = 0.4256 by using Binomial with n=5, p=5/18

Hope that helps