Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a five and then selecting a ten. The probability of selecting a five and then selecting a ten is (Round to three decimal places as needed.)

To find the probability of selecting a five followed by a ten from a standard deck of 52 cards, we start with the probability of drawing a five. There are 4 fives in the deck, so the probability of drawing a five on the first draw is \( \frac{4}{52} \). Once a five has been drawn, there are now 51 cards left in the deck. The number of tens remains at 4. Therefore, the probability of drawing a ten after a five is \( \frac{4}{51} \). The overall probability of both events occurring (drawing a five first and then a ten) is calculated by multiplying these two probabilities: \[ P(\text{five and then ten}) = P(\text{five}) \times P(\text{ten | five}) = \frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = \frac{4}{663} \approx 0.006 \] So, when rounded to three decimal places, the probability of selecting a five and then selecting a ten is approximately 0.006.