IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q9

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.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .