How many totals of seventeen can be made from the numbers on a deck of cards with Face Cards having a value of 10 and Aces having a value of 1 or 11?

Given that:

• There are 4 suits (spades, hearts, diamonds, clubs) per deck.
• Each suit contains 4 cards valued at 10 points (10, Jack, Queen, King)
• Each suit contains one 7

Thus there are 16 10-point cards and 4 7-point cards (64 possible 10+7 combinations)

• Each suit contains one ace and one 6

Thus there are 4 11-point cards and 4 6-point cards (16 possible 11+6 combinations)

Therefore there are 80 possible 2-card combinations totaling 17 points.

For combinations of more than two cards, that's a whole other ball game.