Problem:
From the deck of the 52 cards,cards are drawn randomly without replacement.What is the probability of drawing a king of hearts at the third attempt? If it was drawn at the 15th attempt, what is the probability ?
I have solved the first by finding P(getting the card at third attempt) = P(not getting at first) $\times$ P(not getting at second) $\times$ P(getting at third attempt) = $\frac{51}{52} \times \frac{50}{51} \times \frac{1}{50} = \frac{1}{52}$.
This method seems fine when the times to be drawn is less but for 15 or say for $x$ ... I have solved for $15$ by just writing just two lines in C and got $\frac{1}{52}$, i do agree that 15 is not much big and it may be possible to use this during exam but does there any tricky method exist?