Originally Posted by
ms61853
12*51*50
This corresponds to the number of ways the dealer can be dealt a 2, J, or A on the just the 1st card. The number of ways the dealer can be dealt a 2, J, or A on any card would be:
n(dealt on any card)
= n(dealt on 1st card) + n(dealt on 2nd card) + n(dealt on 3rd card)
- n(dealt on 1st & 3rd cards) - n(dealt on 1st & 2nd cards) - n(dealt on 2nd & 3rd cards)
+ n(dealt on 1st, 2nd, & 3rd cards)
= 12*51*50 + 12*51*50 + 12*51*50 - 12*11*50 - 12*11*50 - 12*11*50 + 12*11*10
= 73,320
which is of course precisely the same figure as that obtained in the above post.