Question

Cards are drawn one 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 the drawn, then show that P,{N=n}= (n-1)(52-n)(51-n) 50×49×17×13 ,where2<n<50 Select the correct answer from above options

Answer 1

Correct Answer - A P(Nth draw gives 2nd ace) =P{1 ace and (n-2) other cards are drawn in (N-1) draws)×P{Nth draw is 2nd ace} = 4.(48)!.(n-1)!(52-n)! (52)!.(n-2)!(50-n)! . 3 (58-n) = 4(n-1)(52-n)(51-n).3 52.51.50.49 = (n-1)(52-n)(51-n) 50.49.17.13