I thought  I knew how to keep score and how many frames were in bowling but,now I'm really messed up.
For all you students of math enjoy.I know I that I'm amazed.
Bowling
   
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BowlingPins

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in the form of a triangle with its vertex oriented towards the bowler. The arrangement of the 10 bowling pins is that of a tetractys and is also triangular number T_4.

Up to two balls (or "bowls") are allowed per "frame," and a game consists of ten frames (with a special rule being used for the number of balls awarded in the last frame). If all pins are knocked down on the first ball, the result is called a "strike," no second ball is awarded for that frame (except in the case of a strike being obtained in the tenth and last frame, in which case two extra balls are awarded), and the number of points tallied is 10 plus the number of pins knocked down on the next two balls. If some or none of the pins are knocked down on the first bowl, then a second ball is awarded. If all the remaining pins are knocked down on the second ball, the result is called a "spare," and the number of points tallied is 10 plus the number of pins knocked down on the bowl of the next ball. If all the pins are not knocked down after bowling two balls in a frame, then the score for that frame is tallied as the total number of pins knocked down.

Ten frames are bowled, unless the last frame contains a strike or spare, in which case an additional bowl is awarded.

The maximum number of points possible, corresponding to 12 strikes, is 300.

The total number of possible bowling games is quite large; there are eleven possibilities for the first ball thrown in the first frame (gutter, 1, 2, ..., 9, strike), and the same possibilities occur for each of the other nine frames. So without considering the second ball in each frame, at a minimum, there are 11^(10) approx 2.6×10^(10) (Balmoral Software). In fact, the true number of games is much larger due to the effect of the second ball in each frame. The total number of possible games is
66^9×241=5726805883325784576 approx 5.7×10^(18)    
(1)

(Cooper and Kennedy 1990).

Define the sets
A={(x,y):0<=x+y<=9} B={(x,y,0)x,y) in A} union {(x,10-x,z):0<=x<=9,0<=z<=10} union {(x,y,z):0<=y<=9,0<=y+z<=10} union {(10,10,z):0<=z<=10}    
(2)

and the matrices
T   =   [sum_((x,y) in A)t^(x+y) 10t^(10) t^(10) 0; sum_((x,y) in A)t^(2x+y) t^(x+10) t^(20) 0; sum_((x,y) in A)t^(2x+2y) 10t^(20) 0 t^(20); sum_((x,y) in A)t^(3x+2y) t^(x+20) 0 t^(30)]   
(3)
C   =   [sum_((x,y,z) in B)t^(x+y+z); sum_((x,y,z) in B)t^(2x+2y+z); sum_((x,y,z) in B)t^(2x+2y+z); sum_((x,y,z) in B)t^(3x+2y+z)]   
(4)
R   =   [1 0 0 0],   
(5)

then a generating function for the number of games s_n corresponding to score n is given by
P(t)=sum_(i=0)^(300)s_it^i,    
(6)

where P(t) is the entry in the 1×1 matrix
RT^9C    
(7)

(Cooper and Kennedy 1990).
BowlingDistribution

The number of possible games s_n with scores n=0, 1, 2, 3, 4, 5, are: 1, 20, 210, 1540, 8855, 42504, ... (Sloane's A060853; Cooper and Kennedy 1990). As can be seen from the figure above, the distribution of number of possible games as a function of n is not precisely symmetric about its maximum. A best-fit Gaussian is given by
s_n=ae^((n-mu)^2/sigma^2),    
(

where a=1.71×10^(17), mu=78.5, and sigma^2=350 (dotted blue curve above).

The mean score is given by
s^_   =   (125572265)/(1574694)   
(9)
   approx    79.7439   
(10)

(Cooper and Kennedy 1990). The mode for the score n=77, namely s_(77)=172542309343732000. For n=288, 289, ..., 300, the totals are 12, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1.

Scores that have the same number of possible ways to be bowled are summarized in the following table.
s_n   n
1   0, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300
11   289, 290
12   287, 288
13   285, 286
14   283, 284
15   281, 282

SEE ALSO: Tetractys, Triangular Number

REFERENCES:

Balmoral Software. "All about Bowling Scores." http://www.balmoralsoftware.com/bowling/bowling.htm.

Cooper, C. and Kennedy, R. E. "A Generating Function for the Distribution of the Scores of All Possible Bowling Games." Math. Mag. 63, 239-243, 1990.

Cooper, C. N. and Kennedy, R. E. "A Generating Function for the Distribution of the Scores of All Possible Bowling Games." In The Lighter Side of Mathematics (Ed. R. K. Guy and R. E. Woodrow). Washington, DC: Math. Assoc. Amer., 1994a.

Cooper, C. N. and Kennedy, R. E. "Is the Mean Bowling Score Awful?" In The Lighter Side of Mathematics (Ed. R. K. Guy and R. E. Woodrow). Washington, DC: Math. Assoc. Amer., 1994b.

Sloane, N. J. A. Sequence A060853 in "The On-Line Encyclopedia of Integer Sequences."



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Weisstein, Eric W. "Bowling." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Bowling.html

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That doesn't relate to keeping score, it relates to how many different scores in different ways are possible.  

If you're trying to figure out how many different scores are possible, I believe it's 301.  0, 1, 2, 3, 4, 5, 6, 7, etc...all the way up to three hundred. (Unless there is a score that is impossible to get...is there?)
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I wanna be a house hack when I grow up.

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I thought there was a score that was impossible to achieve. Don't quote me on it but I thought either 291 or 292 was not possible.