Cards are drawn one at a time, at random, from a well-shuffled full pack of 52 playing cards until 2 aces are obtained for the first time. If \(N\) is the number of cards required to be drawn, then the probability \[P_r\{N=n\}=-\frac1k (n-a)(n-b)(n-c)\] where \(k,a,b,c \in \mathbb Z^+\) with \(a>b>c\). Which of the following options are true?

- (A) \(a=52\)
- (B) \(b=51\)
- (C) \(c=50\)
- (D) 8 is a factor of \(k\)

Enter your answer as a 4 digit string of 1s and 9s, using 1 for correct option, 9 for wrong. For example, 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

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