question_answer

Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn, then \[P\{N=n\},\]where \[2\le n\le 50,\]is

A)  \[\frac{(n-1)\,\,(52-n)\,\,(51-n)}{50\times 49\times 17\times 13}\]

B)  \[\frac{2\,\,(n-1)\,\,(52-n)\,\,(51-n)}{50\times 49\times 17\times 13}\]

C)  \[\frac{3\,\,(n-1)\,\,(52-n)\,\,(51-n)}{50\times 49\times 17\times 13}\]

D)  \[\frac{4\,\,(n-1)\,\,(52-n)\,\,(51-n)}{50\times 49\times 17\times 13}\]

E)  None of these