91Ó°ÊÓ

Let's start by calculating the total number of possible outcomes when drawing four cards in sequence from the deck. There are 52 cards in a standard deck, so for each card we draw, there are 52 possible outcomes. For the second card, there are 51 possible outcomes since one card has already been drawn. Similarly, there are 50 and 49 possible outcomes for the third and fourth cards, respectively. The total number of possible outcomes is the product of these possibilities: \(52 \times 51 \times 50 \times 49\).

Now we need to find the number of outcomes that satisfy the conditions (a spade, a heart, a diamond, and a club in that order). There are 13 spades, 13 hearts, 13 diamonds, and 13 clubs in a deck. For the first card, we have 13 possible spades. Since we're drawing without replacement, after drawing one spade, there will be 12 remaining spades, 13 hearts, 13 diamonds, and 13 clubs in the deck. For the second card, there are 13 possible hearts. After drawing one heart, there will be 12 remaining spades, 12 hearts, 13 diamonds, and 13 clubs in the deck. For the third card, there are 13 possible diamonds. Finally, for the fourth card, there are 13 possible clubs. The number of favorable outcomes is the product of these possibilities: \(13 \times 13 \times 13 \times 13\).

The final step is to calculate the probability of drawing a spade, a heart, a diamond, and a club in that order. We divide the number of favorable outcomes (from step 2) by the total number of possible outcomes (from step 1): Probability = \(\frac{13 \times 13 \times 13 \times 13}{52 \times 51 \times 50 \times 49}\) Now, let's simplify the expression by cancelling some common factors: Probability = \(\frac{1 \times 1 \times 13 \times 1}{4 \times 17 \times 50 \times 7}\) So, the probability of drawing a spade, a heart, a diamond, and a club in that order is: Probability = \(\frac{13}{4 \times 17 \times 50 \times 7} = \frac{13}{23800}\) Thus, the probability of drawing the cards in the desired sequence is \(\frac{13}{23800}\).