# 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.

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