help/confirmation on multi-stage question

consider a random experiment done in 2 stages

first 4 dice are rolled, then a coin is flipped as many times as the number 6 appears

a)find the probability of getting fewer than 2 heads

b)knowing the experiment resulted in fewer than 2 heads, what is the conditional probability that exactly 3 sixes were obtained in the first stage

here is what i have done

a)

probability of getting 1 head = (1/12)(11/12)(11/12)(11/12)

probability of getting 0 head = (11/12)^4

probability of getting fewer than 2 heads = 0.7703

b)

for this, i calculated the probability of getting a certain number of sixes (1, 2, 3 and 4) and then i multiplied those with the probability of getting fewer than 2 heads (respectively)

i finished with this

(5/1296)(1/216)/(0.01663) = 0.001074

I divided by the probability of each set of sixes that would give fewer than 2 heads, that is what the 4 significant digit number is.

I am somewhat confident in my answer to (a), but and Im not too sure about (b). Help, confirmation?