Sum of 6 cards being multiple of 6 I pick 6 cards from a set of 13 (ace-king). If ace = 1 and jack,queen,king = 10 what is the probability of the sum of the cards being a multiple of 6? 
Tried so far:
I split the numbers into sets with values:
6n, 6n+1, 6n+2, 6n+3
like so:
{6}{1,7}{2,8}{3,9}{4,10,j,q,k}{5}
and then grouped the combinations that added to a multiple of 6:
(5c4)(1c1)(2c1) + (2c2)(2c2)(2c2) + (5c4)(2c2) + (5c2)(1c1)(1c1)(2c1)(2c1)
/ (13c6)
= 10/1716
I am almost certain I am missing combinations but am having trouble finding out which.

Your combinations are $4\cdot 4+1\cdot 0+1\cdot 2, 2\cdot 1+2\cdot2+2\cdot3, 4 \cdot 4+2\cdot 1,+$ something that doesn't make sense because there are three places you choose from $1$ and only $0,5$ qualify.  The left number is the number of cards of that value $\pmod 6$ .  You could also have $3\cdot 4+1 \cdot 5+1 \cdot 1+1 \cdot 0, 3 \cdot 4+ 2 \cdot 2 + 1 \cdot 0$ and others
