Find the probability that an ace will appear only in the fifth draw?

Question

Five cards are drawn in succession and without replacement from an ordinary deck of playing cards. Find the probability that an ace will appear only in the fifth draw?

Answer 1

The probability that an ace will not appear in any of the first four draws is

$$\frac{48}{52} \cdot \frac{47}{51} \cdot \frac{46}{50} \cdot \frac{45}{49}$$

The probability of an ace appearing on the last draw is:

$$\frac{4}{48}$$

Just multiply the two results to get the final answer.

Answer 2

first, second , third and fourth draws must not be aces. $\frac{48}{52} $ x $\frac{47}{51} $ x $\frac{46}{50} $ x $\frac{45}{49} $ then you must draw an ace, there are 4 aces and 48 cards left. $\frac{4}{48} $. once computed the answer is 0.0598947271216