We need a perfect hand and 5 specific cards.
Therefore, the valid opening hands are those that contain two of the four Ember Demon cards, both of the Hellforged Axe cards, and one of the two Hellforged Chains cards.
There are 24 valid opening hands.
We need to know how many possible opening hands there are.
*little bit of math :-)
There are 142,506 possible opening hands.
*simple math :-)
Therefore the odds of this hand are a little better than one in six thousand.
The odds for rolling 10 hits when attacking for 10 melee dice is around 16%.