Darts

In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty.

The score of a dart is determined by the number of the region that the dart lands in. A dart landing outside the red/green outer ring scores zero. The black and cream regions inside this ring represent single scores. However, the red/green outer ring and middle ring score double and treble scores respectively.

At the centre of the board are two concentric circles called the bull region, or bulls-eye. The outer bull is worth $25$ points and the inner bull is a double, worth $50$ points.

There are many variations of rules but in the most popular game the players will begin with a score $301$ or $501$ and the first player to reduce their running total to zero is a winner. However, it is normal to play a "doubles out" system, which means that the player must land a double (including the double bulls-eye at the centre of the board) on their final dart to win; any other dart that would reduce their running total to one or lower means the score for that set of three darts is "bust".

When a player is able to finish on their current score it is called a "checkout" and the highest checkout is $170$: T$20$ T$20$ D$25$ (two treble $20$s and double bull).

There are exactly eleven distinct ways to checkout on a score of $6$:

D$3$
D$1$	D$2$
S$2$	D$2$
D$2$	D$1$
S$4$	D$1$
S$1$	S$1$	D$2$
S$1$	T$1$	D$1$
S$1$	S$3$	D$1$
D$1$	D$1$	D$1$
D$1$	S$2$	D$1$
S$2$	S$2$	D$1$

Note that D$1$ D$2$ is considered different to D$2$ D$1$ as they finish on different doubles. However, the combination S$1$ T$1$ D$1$ is considered the same as T$1$ S$1$ D$1$.

In addition we shall not include misses in considering combinations; for example, D$3$ is the same as $0$ D$3$ and $0$ $0$ D$3$.

Incredibly there are $42336$ distinct ways of checking out in total.

How many distinct ways can a player checkout with a score less than $100$?