Sometimes, there's no replacement for just writing them all down. We have two throws, and we'll knock down a different number on our first throw. I'll write down the possibilities in coordinates like (first throw, second throw).
(0,10)
(1,9)
(2,8)
(3,7)
(4,6)
(5,5)
(6,4)
(7,3)
(8,2)
(9,1)
(10,0) <--- doesn't count since that would be a strike!
Counting only the ones that are spares, you'll see there are 10 ways to get a spare (count carefully!)
