This problem doesnt pertain to my study, so don't feel obliged to help out, but its an interesting one imo

[Gif_Goldblum]

So I saw a clip of an online card game. One player had 2 hitpoints and controlled three minions: one with 6 hitpoints, one with 9, and one with 2. Their opponent played a card that deals 14 damage split randomly among all enemies. The question was then asked: what were the odds of none of the shots hitting the opponent?
Note: minions and players don't take more damage than they have hitpoints, and each point of damage is assigned and dealt sequentially.

This is my working, it's just the result I got makes me think I have it all wrong:

Let the total number of permutations = T
Let the number of permutations where no damage hits the player = p
Let the number of permutations where at least one damage hits the player = q

T = 19! / 5! (14 picks from 19 items)
p = 17! / 3! (14 picks from 17 items)
q = T - p = (19! / 5!) - (17! / 3!)

Probability of no damage to player = p / T
Probability of at least 1 damage to player = q / T

Odds of no damage to player = (p / T) / (q / T)
= [ (17! / 3!) / (19! / 5!) ] / { [ (19! / 5!) - (17! / 3!) ] / (19! / 5!) }
= 0.062 (3 dp)
=6.2%

So yeah, I thought it would be much lower than that?