Three 6 sided dice are thrown. What's the probability that the sum of points is 11? And 12?

The given solution is P{11} = 27/216, P{12} = 25/216

My solution is

P{11} = (1,5,5),(5,5,1),(2,4,5),(5,4,2)/6^3 = (1,5,5),(5,5,1),(2,4,5),(5,4,2)/216

P{12} = (1,5,6),(6,5,1),(2,4,6),(6,4,2),(3,4,5),(5,4,3)/6^3 = (1,5,6),(6,5,1),(2,4,6),(6,4,2),(3,4,5),(5,4,3)/216

Problem 2

n six sided dice are thrown. Calculate the probability, that the sum of points that come up is no lesser than 6n - 1

The given solution is n+1/6^n

I don't understand this one

Problem 3

Two six sided dice are thrown. What's the probability that the sum of points is an even number?

The given solution is 3x3+6x3/6^2 = 0,75

My solution is based on a previous thread, with the difference that one die is thrown 2 times

2,4,6,8,10,12

There are:

(1,1) ways to get 2

(1,3)(3,1)(2,2) to get 4

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

(3,5)(5,3)(2,6)(6,2)(4,4) to get 8

(4,6)(6,4)(5,5) to get 10

(6,6) to get 12

=> 1+3+5+5+3+1/36 = 18/36 = 1/2 = 0,5

Problem 4

From an urn, which contains balls with the numbers 1,2,...,N, we subtract 1 ball n times. Calculate the probability that the numbers of the balls that are subtracted, written in the order of subtraction, form a growing row, if after every subtraction, the subtracted ball:

a) returns to the urn before the next subtraction

b) doesn't return to the urn

The given solution is:

a) CN^k/N^k

b) 1/n!

Don't understand this one either

Problem 5

n dice are thrown. Calculate the probability that n1 ones, n2 twos,...,n6 sixes come up, when n1+n2+...+n6 = n

The given solution is

n!/n1!*n2!*...*n6!*6^n

I don't understand this one