[AaronBrown]

Baker350 has the right idea, but the trouble is the events are not independent. If you know a line contains at least one "h" then it's less likely to contain an "e". However, once we do one line, then we can use independence for the rest of the problem.

Here's one way to do it.

(1) Start by counting all "h," "e" and "s" as a single letter with 3/26 probability of coming up. Compute the probability of getting 0, 1, 2 and up to 36 of these in a 36 letter line.

(2) For each number in (1), compute the probability that you have at least one each of each letter. Obviously that's 0 for 0, 1 and 2.

(3) Also for each number in (1), combine "u" and "w" as one letter with 2/26 probability of coming up. Compute the probability of getting at least one of these in the remaining letters in the line.

(4) Multiply the probabilities in (2) and (3), then sum for all the numbers from 0 to 36.

Then continue as Baker350 did.