Circus of Luck 4

Larry enters a newly opened circus which houses $11$ tents (Tent $A, B, C, ... , K$ ) that each features a free-to-play game. The game of Tent $A$ involves a computer that will flash one from $2$ symbols. If the contestant guesses what symbol will be flashed, he wins $2\$$ . The game of Tent $B$ involves a computer that will flash one from $3$ symbols. If the contestant guesses what symbol will be flashed, he wins $3\$$ . The game of Tent $C$ involves a computer that will flash one from $4$ symbols. If the contestant guesses what symbol will be flashed, he wins $4\$$ . And so on. $\text{Tent} \space A \space (\dfrac{1}{2} \space \text{chance of winning}, \space 2\$ \space \text{prize}), \space \text{Tent} \space B \space (\dfrac{1}{3} \space \text{chance of winning}, \space 3\$ \space \text{prize}), \space \text{Tent} \space C \space (\dfrac{1}{4} \space \text{chance of winning}, \space 4\$ \space \text{prize}), \space ... \space , \space \text{Tent} \space K \space (\dfrac{1}{12} \space \text{chance of winning}, \space 12\$ \space \text{prize})$

Let's say a "scenario" is the experience of Larry playing in the circus (winning all the games, winning all except Tent $F$ , losing all games, etc.)

Question : If Larry plays all games once each, how many scenarios would there be where he wins any amount of games?

Try Circus of Luck 1